GameNets 2009 Final Program and Book of Abstracts

International Conference on Game Theory for Networks, 13-15 May 2009, Boğaziçi University, Istanbul, Turkey

Organized by Boğaziçi University and ICST

Financial co-sponsors:

Technical co-sponsors:

Program at a Glance

May 13th

Wednesday

May 14th Thursday

May 15th Friday

08:30 09:00 Registration

09:00 09:30 Opening Remarks

09:30 10:30

Plenary Talk: R. Aumann

Plenary Talk: C. Cannings

Plenary Talk: S. Goyal

10:30 11:15 Coffee and Tea Break

11:15 12:45

Cooperative Games

Power Control I

Emerging Communication

Networks Learning Evolutionary

Games

Game Theoretic Network Models II

Stochastic Games

Wireless Networks II Pricing

12:45 14:00 Lunch

14:00 15:30

Game Theoretic Network Models I

Power Control

II

Equilibrium Analysis

Spectrum Sharing

II

Game Theoretic Network

Models III

Wireless Networks

III

15:30 16:00 Coffee and Tea Break Coffee and Tea Break

16:00 17:30

Spectrum Sharing

I

Random Access Games

Wireless Networks

I

Game Theoretic

Analysis of Auctions and

Network Security

P2P and Social

Networks

Wireless Networks

IV

Game Theoretic Network

Models IV

Security Games

A Message from the General Chair: Tamer Başar

There may not be a consensus on exactly when game theory or game-theoretic thinking supported by systematic analysis was born (some consider the starting point to be John Von Neumann’s proof of the minimax theorem in “Zur theorie der Gesellschaftspiele” in 1928, others view the inception the publication of the 19th century work of André-Marie Ampère titled “Considérations sur la théorie mathématique du jeu”, inspired by the 18th century work “Essai d’Arithmétique Morale” by Georges Louis Buffon, and some take it to even earlier times), but it is without dispute that John Von Neumann and Oskar Morgenstern’s 1944 book “Theory of Games and Economic Behavior” propelled the extensive research activities in both cooperative and non-cooperative game theory in the second half of the 20th century, which continue today with an even higher intensity, finding applications not only in economics, but also in political science, sociology, psychology, engineering, computer science, communications, and transportation, to name just a few. All these application areas benefit from the mathematically rigorous and conceptually satisfying framework of game theory, which studies complex interactions among interdependent (rational) players.

Recently, there has been a surge in research activities that employ game theory to model and analyze the performance of various networks, such as communication networks, computer networks, social networks, biological networks, molecular networks, and neural networks. There already exist several successful instances where game theory provides a deeper understanding of complex network dynamics and leads to a better design of efficient, scalable, and robust networks. Still, there remain many interesting open research problems yet to be identified and explored, and many issues to be addressed. Moreover, studies of different networks heretofore have largely been performed independently, although in many cases it is apparent that they share many similarities in terms of problem structures and the technical challenges they offer. Bringing these different communities together, and identifying and addressing new research problems cutting across different disciplines are among the main goals of this truly interdisciplinary as well as multidisciplinary conference, GameNets 2009.

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This three-day conference (May 13-15) is being held on the beautiful campus of Boğaziçi University (my alma mater, called at the time Robert College), in Istanbul, Turkey. It brings together researchers who apply game theory to analyze, design, and assess the performance of networks. In organizing GameNets, and shaping its technical program, we have recognized the synergies between various related research areas, and have created a forum for discussions regarding the benefits and limitations of game theory as a performance assessment and design tool for networks. Both the application of game theory to networking problems and the development of new game-theoretic methodologies that can be applied in that context are included in the program.

The conference features three plenary talks, covering different aspects of game theory and its various applications. The plenary speakers are Nobel Laureate Robert Aumann from the Hebrew University of Jerusalem, Israel (speaking on Rational Expectations in Games), Chris Cannings from the University of Sheffield, England (speaking on The Majority and Minority Models on Regular and Random Graphs), and Sanjeev Goyal from Cambridge University, England (speaking on Strategic Network Formation). I thank them for accepting my invitation to deliver the plenary addresses on each of the three days of the conference. In addition to the three plenary sessions, there are 23 regular sessions, which include contributed as well as invited papers. I want to thank the Technical Program Committee Co-Chairs Jianwei Huang and Rayadurgam Srikant for their efforts, which led to a top-quality technical program that also meets the goals initially set for the conference. Other members of the organizing committee also made essential contributions to GameNets in various stages of its organization, and I thank them for freely devoting their time and energy toward success of the conference: Tansu Alpcan, as Publicity Chair, created the GameNets website, and constantly updated it as various new information became available, helping also with trouble-shooting in connection with the conference’s paper management system; Kıvanç Mıhçak acted as Local Arrangements Chair and in this capacity arranged hotel accommodation for participants and the social events, by working also with the local organizing company; Mehmet Akar, as Finance and Registration Chair, handled very ably all financial matters related to the conference, as well as registration, in addition to helping with local arrangements; Hitay Özbay, as Publications Chair, was in charge of receiving from the authors the final versions of accepted papers and turning them on a fast track into this proceedings volume made available at the conference. I also want to acknowledge the contributions of my secretary, Becky Lonberger, who was the glue that

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connected and held together various activities in different domains, and who also interfaced with ICST and particularly Maria Morozova. I also appreciated the advice provided by the Steering Committtee, chaired by Imrich Chlamtac, whose members were Eitan Altman, Anthony Ephremides, and Thomas Vincent.

We were able to hold the registration fees for the conference at record low levels, while providing maximum return to the participants (such as free transportation, lunches on all three days, welcoming reception/dinner, and gala banquet on a boat (for full registrants)), all thanks to the generous support of various organizations in Turkey. First and foremost I want to express my gratitude to Boğaziçi University and its President (Rector) Kadri Özçaldıran, for hosting the conference on their campus by providing free access to space and facilities, and for co-sponsoring plenary sessions. Bilgi University also provided generous financial sponsorship, and I thank particularly Remzi Sanver from that university for arranging the support. The sponsorship of the Central Bank of Turkey provided essential support for various expenses associated with the conference, and subsidized the conference banquet planned on a yacht cruising the waters of Bosphorous. And finally, TUBITAK (The Scientific and Technological Research Council of Turkey) provided funds for various local expenses, including producing and printing of the conference material. In their roles as technical co-sponsors, we appreciated associations with the IEEE Control Systems Society and CREATE-NET.

I welcome you all to this exciting event, and wish you a productive meeting. I also hope that you have reserved some time before and/or after the conference (as well as on Thursday afternoon when we have a break from the sessions) to explore the magnificent city of Istanbul – the largest city proper in Europe; the cultural and financial center of Turkey; and cradle to multiple civilizations over its 2,000 years of history, with the early settlements going as far back as 6,500 BC. This will be a unique opportunity to blend in some culture to your conference visit.

Tamer Başar General Chair

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Organized by:

Financial Co-Sponsors

Technical Co-Sponsors

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A Message from the Technical Program Committee Co-Chairs

Welcome to GameNets 2009, the first International Conference on Game Theory for Networks. GameNets had been held as a small workshop in the past, but the increasing importance of game theory in the study of networks has generated sufficient interest to hold a full-fledged conference on the topic. This first edition of the conference attracted about 90 submissions applying game-theoretic concepts to many different types of networks including wireless networks, social networks and biological networks. The selection of papers for the conference program was primarily based on the reviews of an outstanding Technical Program Committee (TPC). The TPC consisted of 33 experts from all over the world. Each paper received at least three reviews from the TPC members. Based on this input, 53 papers were accepted for inclusion in the conference program. In addition to the contributed papers, a number of invited sessions were organized by the following leading researchers in game theory: Pierre Bernhard (UNSA), Randall Berry (Northwestern), Rachid El Azouzi (Avignon), Yezekael Hayel (Avignon), Zhu Han (Houston), Michael Honig (Northwestern), George Kesidis (Penn State), Narayan Mandayam (Rutgers), Asu Ozdaglar (MIT), Daniel Palomar (HKUST), Srinivas Shakkottai (Texas A&M), Corrine Tuoati (INRIA), and Honggang Zhang (Suffolk). Due to the efforts of these session organizers, the conference program includes 47 invited papers. We express our sincere thanks to the TPC members and the invited session organizers for their invaluable help in putting together the program. In addition to the contributed and invited papers, the conference program includes plenary lectures by three distinguished game theorists: Prof. Robert Aumann (Hebrew University of Jerusalem), Prof. Chris Cannings (University of Sheffield) and Prof. Sanjeev Goyal (University of Cambridge). We thank them for participating and contributing to the program. We hope that you find the conference stimulating and enjoy the technical program. Thank you all for participating in GameNets and making it a success.

Jianwei Huang and Rayadurgam Srikant Technical Program Committee Co-Chairs

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General Chair

Tamer Başar, Univ Illiniois at Urbana-Champaign, USA

Technical Program Committee Co-Chairs

Jianwei Huang, The Chinese University of Hong Kong, Hong Kong Rayadurgam Srikant, Univ Illiniois at Urbana-Champaign, USA

Local Arrangements Chair

Kıvanç Mıhçak, Boğaziçi Univ, Turkey

r

M

Tansu A

Rebecca Lon

Finance and Registration Chai

ehmet Akar, Boğaziçi Univ, Turkey

lpcan, D

Hitay Ö

Ma

berger, U

Publicity Chair

eutsche Telekom Labs, Germany

r

Publications Chai

Organizing Committee

zbay, Bilkent Univ, Turkey

r

Conference Coordinato

ria Morozova, ICST

Conference Secretary

niv Illiniois at Urbana-Champaign, USA

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Program Committee

Tansu Alpcan Mingyan Liu

Eitan Altman Tom Luo

Gürdal Arslan Allen MacKenzie

Mario Cagalj Ravi Mazumdar

Peter Caines Jacqueline Morgan

Mung Chiang Aris Moustakas

Costas Courcoubetis Y. Narahari

Munther Dahleh Steven Patek

Luiz Dasilva Lacra Pavel

Alfredo Garcia Volkan Rodoplu

Josef Hofbauer Gesualdo Scutari

Zhu Ji Jeff Shamma

George Kesidis Anthony So

Sunil Kumar Kevin Tang

Kevin Kwiat Yang Yang

Amir Leshem Honggang Zhang

XiangYang Li Chi Zhou

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Steering Committee

Steering Committee Chair

Imrich Chlamtac, CREATE-NET, Italy

Steering Committee Members

Eitan Altman, INRIA, France

Anthony Ephremides, Univ Maryland, USA

Thomas L. Vincent, Univ Arizona, USA

Session Organizers

Rachid El Azouzi Narayan Mandayan

Pierre Bernhard Daniel Palomar

Randall Berry Asuman Özdağlar

Zhu Han Srinivas Shakkottai

Hayel Yezekael Corinne Tuoati

Michael Honig Honggang Zhang

George Kesidis

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General Information

Conference Venue

All sessions of “International Conference on Game Theory for Networks” will be held at Boğaziçi University (BU) South Campus. Plenary talks will be held at Albert Long Hall. The Technical sessions will be held at the top floor of the Perkins Hall (The Faculty of Engineering).

Boğaziçi University (Turkish: Boğaziçi Üniversitesi) is one of the most prominent educational institutions in Turkey. It was established in 1971 on the campus of Robert College, which, in turn, was established in 1863 as the first American school outside of the United States. The university is located on the European side of the Bosphorus in İstanbul (hence the name, which means 'Bosphorus University').

İstanbul, historically Byzantium and later Constantinople; is Europe's most populous city (the world's 4th largest city proper and 19th largest urban area) and Turkey's cultural and financial center. The city covers 27 districts of the Istanbul province. It is located on the Bosphorus Strait, and encompasses the natural harbor known as the Golden Horn, in the northwest of the country. The city was chosen as joint European Capital of Culture for 2010. The historic areas of Istanbul were added to the UNESCO World Heritage List in 1985. Address : Boğaziçi Üniversitesi, Bebek 34342, İstanbul, Turkey Tel : 0212 359 54 00 Web : http://www.boun.edu.tr/ Language

The native language in Turkey is Turkish, but the language of this conference will be English. Simultaneous translation will not be provided.

Currency

The Turkish monetary unit is “Turkish Lira”. The exchange rates can be learned at the information desks of the hotels or at exchange offices nearby. As of April 21, 2009, 1 US dollar is equivalent to 1.62 Turkish Lira, and 1 Euro is equivalent to 2.10 Turkish Lira.

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Transportation

A shuttle service between the conference hotels (Sheraton, Bilek and Niza) and the conference site will be available.

The buses will leave from Sheraton at 8:00 on Wednesday morning and at 8:30 on Thursday and Friday mornings. Pick-ups from Bilek Hotel and Niza Hotel will be made on the way.

South Campus Map

40 – ETİLER GATE (Main Gate) 3- ALBERT LONG HALL (Plenary Talks)

14- PERKINS HALL - The Faculty of Engineering (Technical Sessions on the top floor)

23 – KENNEDY LODGE (Welcome Reception)

Important Events

Opening Ceremony May 13th, Wed, 09:00 – 09:30 @ Albert Long

Welcome Reception May 13th, Wed, 18:30 – 22:30 @ Kennedy Gala Dinner : May 15th, Friday, 19:30-24:00, Boat Tour,

Buses leave from Boğaziçi Univ. @ 18:30

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Plenary Talks

RATIONAL EXPECTATIONS IN GAMES 13-May-2009, 09.30-10.30, Albert Long Hall, Boğaziçi University

Robert J. Aumann, The Hebrew University of Jerusalem, Israel

Abstract : A player i’s actions in a game are determined by her beliefs about other players; these depend on the game’s real-life context, not only its formal description. Define a game situation as a game together with such beliefs; call the beliefs—and i’s resulting expectation—rational if there is common knowledge of rationality and a common prior. In two-person zero-sum games, i’s only rational expectation is the game’s value. In an arbitrary game G, we characterize i’s rational expectations in terms of the correlated equilibria of the doubled game 2G in which each of i’s strategies in G appears twice. (This keynote address is based on a paper with the same title, and co-authored with Jacques H. Dreze (Center for Operations Research and Econometrics, Université Catholique de Louvain, 34 Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium), which appeared in American Economic Review, 98:1, 72-86, 2008.) Biographical Sketch:

Robert Aumann was born in 1930, in Frankfurt am Main, Germany, to a well-to-do orthodox Jewish family. Fleeing Nazi persecution, he emigrated to the United States with his family in 1938, settling in New York. In the process, his parents lost everything, but nevertheless gave their two children an excellent Jewish and general education. Aumann attended Yeshiva elementary and high schools, got a

bachelor's degree from the City College of New York in 1950, and a Ph.D. in mathematics from MIT in 1955. He joined the mathematics department at the Hebrew University of Jerusalem in 1956, and has been there ever since. In 1990, he was among the founders of the Center for Rationality at the Hebrew University, an interdisciplinary research center centered on Game Theory, with members from over a dozen different departments, including Business, Economics, Psychology, Computer Science, Law, Mathematics, Ecology, Philosophy, and others. Aumann is the author of ninety research papers and six books, and has held visiting positions at Princeton, Yale,

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Berkeley, Louvain, Stanford, Stony Brook, and NYU. He is a member of the American Academy of Arts and Sciences, the National Academy of Sciences (USA), the British Academy, and the Israel Academy of Sciences; holds honorary doctorates from the Universities of Chicago, Bonn, Louvain, City University of New York, and Bar Ilan University; and has received numerous prizes, including the Nobel Memorial Prize in Economic Sciences for 2005. Aumann is married and has five children (the oldest was killed in Lebanon in 1982), twenty-one grandchildren, and five great-grandchildren. When not working, he likes to hike, ski, cook, and study the Talmud.

THE MAJORITY GAME ON REGULAR AND RANDOM NETWORKS

14-May-2009, 09.30-10.30, Albert Long Hall, Boğaziçi University

Chris Cannings, University of Sheffield, United Kingdom Abstract : In the two strategy majority/minority game on a network, at time t, an individual observes some subset of its neighbors’ strategies, and then adopts at time t+1 that strategy which was more/less frequently played by its neighbors at time t. We shall examine in this paper a variety of distinct models which vary the subsets observed, the synchrony of actions, the regularity, or otherwise, of the networks, the mix of majority and minority players. Important measures of the dynamics of such systems such as the nature of the fixed points, and limit cycles are discussed. The expected payoffs under certain games are computed and compared. In particular we shall examine complete networks, hypercubes and a certain class of cubic networks. These graphs have rather different numbers of symmetries which impact on the properties of the dynamics. The work is of an exploratory nature and hopefully will suggest many potential lines of enquiry. Biographical Sketch:

Chris Cannings is an Emeritus Professor at the University of Sheffield, UK having previously held appointments at the Universities of Aberdeen, UK and Pavia, Italy and visiting positions at Stanford, Cambridge and Utah. He is a member of the Peer Review College of the U.K. Engineering and Physical Sciences Council, the College of Experts of the U.K. Medical Research

Council, and an Expert for the Institut de la Santé et de la Recherche Médicale, France. With David Balding and Martin Bishop he is editor of the Handbook of Statistical Genetics. His research focuses on the mathematical modelling of biological processes, particularly

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population genetics and evolution. His main contributions have (perhaps) been, single locus models of selection (e.g. [1], [2]), the introduction of the exchangeable model of random genetic drift (e.g. [3], [4]), the development of the “peeling” algorithm for calculations on complex genealogies [5], analysis of the War of Attrition (e.g. [6], [7]), the study of the patterns of Evolutionary Stable Strategies for finite conflicts (e.g. [8], [9]), and aspects of enumeration and simulation of genealogies [10], [11]. Current work is on dynamics of, and on, networks, particularly in Amorphic Computing, where randomly linked microprocessors can self-assemble to perform various tasks (www.amorph.group.shef.ac.uk). [1] Cannings, C. (1967) Equilibrium, convergence and stability at a sex-linked locus under natural selection, Genetics, 56, 613-618 [2] Cannings, C. (1971) Natural selection at a multi-allelic autosomal locus with many niches, J.Genet., 60, 255-259. [3] Cannings, C. (1974) The latent roots of certain Markov chains arising in genetics; a new approach. 1. Haploid models. Adv.Appl.Prob., 6, 260-290. [4] Cannings, C. (1975) The latent roots of certain Markov chains arising in genetics: A new approach II. Further haploid models'. Adv.Appl.Prob., 7, 264-282. [5] Cannings, C., E.A.Thompson and M.H.Skolnick. (1978) Probability functions on complex pedigrees. Adv.Appl.Prob., 10, 26-61. [6] Bishop, D.T. and C.Cannings. (1978) A generalized war of attrition. J.Theoret.Biol., 70, 85-125 [7] Bishop, D.T., C. Cannings and J.Maynard Smith. (1978) The war of attrition with random rewards. J.Theoret. Biol. 74, 377--388. [8] Vickers, G.T. and C.Cannings. (1988) Patterns of ESS's. I., J.Theoret.Biol., 132, 387-408. [9] Cannings, C. and G.T.Vickers. (1988) Patterns of ESS's. II., J.Theoret.Biol., 132, 409-420. [10] Camp, N.J., Cannings, C and Sheehan, N.A. (1994) The number of genotypic assignments on a genealogy 1. The method and simple examples. IMA Journal of Mathematics Applied in Medicine and Biology,11,95-106. [11] Cannings, C and A.W.Thomas, (2007) Inference, Simulation and Enumeration of Genealogies. pp 781-805. In Handbook of Statistical Genetics , Ed. D.Balding, M.Bishop and C.Cannings.

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STRATEGIC NETWORK FORMATION

15-May-2009, 09.30-10.30, Albert Long Hall, Boğaziçi University

Sanjeev Goyal, University of Cambridge, United Kingdom Abstract : The theory of strategic network formation has been one of the most lively subjects of research in theoretical economics in the last decade. The aim of this talk is to provide a survey of this theory and to highlight some of important open questions.

Biographical Sketch: Sanjeev Goyal was born in Moradabad and spent his early years in the eastern province of Assam, India. He was educated at the University of Delhi, the Indian Institute of Management, Ahmedabad and did doctoral work leading to a PhD at Cornell University, in the United States. He has held Professorships at Erasmus University Rotterdam, University of London and University of Essex, and is currently Professor of

Economics and Fellow of Christ's College, Cambridge. Sanjeev Goyal is one of the pioneers in the economic study of networks; his research has appeared in leading international journals such as Econometrica, Review of Economic Studies and Journal of Political Economy. His book `Connections: An introduction to the economics of networks' was published by Princeton University Press in 2007.

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1A1 Cooperative Games 11:15-12:45 Chair: Stefano Buzzi

1A1.1 Cooperative Game Theoretic Approach to Integrated Bandwith Sharing and Allocation, Manzoor Ahmed Khan, Ahmet Cihat Toker, Cuong Troung, Fikret Sivrikaya, Sahin Albayrak The current trend in wireless communication networks involves the integration of different wireless access technologies into a single operator network. The possible leveraging of high deployment costs, and the possibility to increase revenue have also introduced the concept of network sharing between different operators. The problem of optimal allocation of bandwidth to multimedia applications over different wireless access networks, is augmented with the possibility of using the bandwidth of other operators who are willing to share bandwidth. We formulate the allocation of bandwidth within the operator network and distribution of excess bandwidth among operators as cooperative bargaining games. We provide distribution and allocation rules based on the Kalai Smorodinsky Solution, and provide bandwidth offer algorithms based on these rules. We compare this integrated approach with the service and capacity based approaches in the literature. 1A1.2 Coalition Formation through Learning in Autonomic Networks, Tao Jiang, John S. Baras Autonomic networks rely on the cooperation of participating nodes for almost all their functions. However, due to resource constraints, nodes are generally selfish and try to maximize their own benefit when participating in the network. Therefore, it is important to study mechanisms, which can be used as incentives for cooperation inside the network. In this paper, the interactions among nodes are modelled as games. A node joins a coalition if it decides to cooperate with at least one node in the coalition. The dynamics of coalition formation proceed via nodes that interact strategically and adapt their behavior to the observed behavior of others. We present conditions that the coalition formed is stable in terms of Nash stability and the core of the coalitional game. 1A1.3 Minimum Cut Tree Games, Anne M. Schwahn In this paper we introduce a cooperative game based on the minimum cut tree problem which is also known as multi-terminal maximum flow problem. In a routing situation a network with capacities induced by vertices of a coalition has to be substituted by a network providing the same capacity for non-simultaneous flows but having a minimum number of edges and minimum total capacity. The solutions to this requirement are exactly the minimum cut trees. Minimum cut tree games are shown to be totally balanced and a solution in their core can be obtained in polynomial time. This special core allocation is closely related to the solution of the original

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graph theoretical problem. We give an example showing that the game is not supermodular in general, however, it is for special cases and for some of those we give an explicit formula for the calculation of the Shapley value. 1A1.4 Decentralized Decision Making Process for Document Server Networks, Aurélie Beynier, Abdel-Illah Mouaddib, A peer-to-peer server network system consists of a large number of autonomous servers logically connected in a peer-to-peer way where each server maintains a collection of documents. When a query of storing new documents is received by the system, a distributed search process determines the most relevant servers and redirects the documents to them for processing (compressing and storing at the right document base). In this paper, we model this distributed search process as a distributed sequential decision making problem using a set of interactive Markov Decision Processes (MDP), a specific stochastic game approach, which represent each server’s decision making problem. The relevance of a server to a document is regarded as a reward considering the capacity of the storage and the goodness score of a server. We show that using a central MDP to derive an optimal policy of how to distribute documents among servers leads to high complexity and is inappropriate to the distributed nature of the application. We present then interactive MDPs approach transforming this problem into a decentralized decision making process.

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1A2 Power Control I 11:15-12:45 Chair: Tansu Alpcan

1A2.1 A Noncooperative Approach to Joint Rate and Power Control for Infrastructure Wireless Networks, Giacomo Bacci, Marco Luise

This paper shows how to tailor a game-theoretic approach to the issue of distributed resource allocation in a multiple-access wireless network with different quality of service constraints. According to the nature of the terminals (either fixed/vehicular or mobile/battery-powered, in one respect, and either licensed or unlicensed in another), each user pursues a different goal in the network. Game theory is used as a possible tool to ensure optimum coexistence of users with highly conflicting interests. In the proposed game, each user is allowed to jointly set its transmit power and data rate according to a utility-maximizing criterion, where the utility is defined as the ratio of the overall throughput to the transmit power. The noncooperative Nash solution of the game is investigated and closed-form expressions for this equilibrium are derived and compared with numerical results for a decentralized resource control algorithm.

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1A2.2 Uplink Power Control and Base Station Association in Multi-channel Cellular Networks, Chandramani Singh, Anurag Kumar, Rajesh Sundaresan

A combined base station association and power control problem is studied for the uplink of multichannel multicell cellular networks, in which each channel is used by exactly one cell (i.e., base station). A distributed association and power update algorithm is proposed and shown to converge to a Nash equilibrium of a noncooperative game. We consider network models with discrete mobiles (yielding an atomic congestion game), as well as a continuum of mobiles (yielding a population game). We find that the equilibria need not be Pareto efficient, nor need they be system optimal. To address the lack of system optimality, we propose pricing mechanisms. It is shown that these mechanisms can be implemented in a distributed fashion.

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1A2.3 Power Games in MIMO Interference Systems, Gürdal Arslan, M. Fatih Demirkol, Serdar Yüksel We consider a multi-link and multi-input-multioutput (MIMO) interference system in which each link wishes to minimize its own power by choosing its own signal vector subject to an information theoretic Quality-of-Service (QoS) requirement. Our setup leads to a multi-link game, referred to as a “power game”, in which the feasible strategy set of an individual link depends on the strategies of the other links. We characterize the rates for which an equilibrium solution exists in a power game in terms of the equilibria of “capacity games” introduced in our earlier work [1]. We provide an example where the set of equilibrium rates is properly contained in the set of achievable rates. We provide a conservative estimate of the region of equilibrium rates using a minmax approach. We discuss the uniqueness of equilibrium as well as the convergence of best response dynamics (a.k.a. iterative water-filling) for all rates when the interference is sufficiently small and some other mild conditions are met. Finally, we extend our results to the case where the QoS requirements are softened. 1A2.4 Distributed Power Control using Non-monotonic Reaction Curves, Ömür Özel, Elif Uysal Bıyıkoğlu In this paper, we study distributed power control in an interference network. In particular, distributed power control mechanisms are devised by exploiting a one-shot noncooperative game based on a suitably chosen utility function. The utility is a function of quality of service (QoS) objectives defined in terms of fading-induced outage probabilities. Equilibrium analysis of the resulting power control game is made, and its relationship with admission control is discussed. The main contribution of the paper is a mechanism for obtaining smooth non-monotonic reaction curves, in contrast to sharp cut-offs with increasing interference that are characteristic of admission control. This is done via the introduction of a factor fd(.) into the

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utility function, allowing users to smoothly decrease their objectives in response to interference. The resulting algorithm is called non-monotonic power control (NMPC). We provide sufficient conditions for a unique Nash equilibrium (NE) under NMPC. The equilibria are studied in numerical examples, which exhibit that NMPC increases the number of users who achieve their objectives, without removing any user, as compared to previous utility-based power control algorithms with harsher reaction curves. Considerable energy efficiency is gained by a transfer of resources from the disadvantaged user to the advantaged: users whose SIR objectives are infeasible under current channel gains reduce their own transmit power thus helping on others. We view this solution as an attractive alternative to pricing in wireless networks formed by cooperative nodes (such as sensor networks) where an economic model is not natural.

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1A3 Emerging Communication Networks 11:15- 12:45 Chair: Tristan Tomala

1A3.1 Oblivious Equilibrium: An Approximation to Large Population Dynamic Games with Concave Utility, Sachin Adlakha, Ramesh Johari, Gabriel Weintraub, Andrea Goldsmith We study stochastic games with a large number of players, where players are coupled via their payoff functions. A standard solution concept for such games is Markov perfect equilibrium (MPE). It is well known that the computation of MPE suffers from the “curse of dimensionality.” Recently an approximate solution concept called “oblivious equilibrium” (OE) was developed by Weintraub et. al, where each player reacts to only the average behavior of other players. In this work, we characterize a set of games in which OE approximates MPE. Specifically, we show that if system dynamics and payoff functions are concave in state and action and have decreasing differences in state and action, then an oblivious equilibrium of such a game approximates MPE. These exogenous conditions on model primitives allow us to characterize a set of games where OE can be used as an approximate solution concept. 1A3.2 A Hierarchical Spatial Game Over Licensed Resources, Gaurav Kasbekar, Eitan Altman, Saswati Sarkar We consider a scenario in which a regulator owns the spectrum in a region. Two service providers lease spectrum from the regulator and set up a base station each to serve mobile subscribers. This leads to a hierarchical game with players at two levels- the mobile subscribers at level 1 and the service providers at level 2. In the game at level 1, each mobile subscriber chooses a service provider to subscribe to and whether to be a primary subscriber of its service provider and receive high-priority service or to be a secondary subscriber and receive low-priority service. In the game at level 2, each

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service provider chooses the quantity of spectrum to lease from the regulator and the rates at which to charge its mobile subscribers for the throughput they receive. We first analyze the game at level 1 for different models and in each case show the existence of a threshold-type Wardrop equilibrium, in which there exist thresholds that divide the region into sets of mobile subscribers that make the same decision at equilibrium. Next, assuming that the mobile subscribers act so as to give rise to the equilibrium found above, we analyze the game at level 2 and show the existence of a Nash equilibrium.

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1A3.3 Asynchronous Gossip Algorithms for Stochastic Optimization, S. Sundhar Ram, Angelia Nedić, Venugopal Veeravalli We consider a distributed multi-agent network system where the goal is to minimize an objective function that can be written as the sum of component functions, each of which is known (with stochastic errors) to a specific network agent. We propose an asynchronous algorithm that is motivated by a random gossip scheme where each agent has a local Poisson clock. At each tick of its local clock, the agent averages its estimate with a randomly chosen neighbor and adjusts the average using the gradient of its local function that is computed with stochastic errors. We investigate the convergence properties of the algorithm for two different classes of functions: differentiable but not necessarily convex and convex but not necessarily differentiable. 1B1 Game Theoretic Network Models I 14:00-15:30 Chair: Roland Malhame

1B1.1 Reliable Relaying with Uncertain Knowledge, Jiwoong Lee, Jean Walrand The motivation for this paper is to analyze the effect of information uncertainty on the design and performance of protocols. The paper considers two types of situation. The first is when different nodes in the network have bounded knowledge about what other nodes know. The second, called common knowledge about inconsistent beliefs, is when the information is inconsistent but everyone knows it. Situations of bounded or inconsistent information arise naturally in networks because the state of these systems changes and nodes takes time to learn of those changes. The specific problem that the paper explores is the relaying of packets in a simple butterfly network. Despite its apparent simplicity, this problem enables to illustrate key features of situations of uncertain knowledge that arise in networks. The paper presents two impossibility facts and one possibility fact, in the latter of which a scheme that enables optimal coordination given persisting imperfection in knowledge is introduced.

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1B1.2 N-Player Cournot and Price-Quantity Function Mixed Competition, Shuang Wu, John Musacchio We study the value of network providers committing to offering a quantity of bandwidth to a market versus having the amount of bandwidth offered be conditional on the prices that the market settles upon. For instance a cable television ISP has the option to shift capacity from Internet service to television channels if the market price for Internet service is low, and thus such a provider can avoid committing to a fixed capacity being devoted to Internet service. To study the issue, we consider a two-stage game. In the first stage, competing network providers either commit to set a quantity of bandwidth to offer to the market, or choose to offer bandwidth to the market according to a function relating price to quantity. If they choose the later option, the network provider initially chooses a slope for their function. In the second stage, the quantity players choose the quantity to offer, where as the function players choose the offset term of their function. We show that a unique Nash equilibrium exists for the second stage play, and that it is the only subgame-perfect equilibrium for each provider to choose a quantity commitment in the first stage. We also show that a quantity commitment is not always a subgame-perfect equilibrium when demand uncertainty is introduced to the model.

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1B1.3 Traffic Engineering, Content Distribution, and Continuous Potential Games, Dominic DiPalantino, Ramesh Johari We explore the interaction between content distribution and traffic engineering. Because a traffic engineer may be unaware of the structure of content distribution systems or overlay networks, his management of the network does not fully anticipate how traffic might change as a result of his actions. Content distribution systems that assign servers at the application level can respond very rapidly to changes in the routing of the network. Consequently, the traffic engineer’s decisions may almost never be applied to the intended traffic. We use a game-theoretic framework in which infinitesimal users of a network select the source of content, and the traffic engineer decides how the traffic will route through the network. We formulate a game and prove the existence of equilibria. Additionally, we present a setting in which equilibria are socially optimal, essentially unique, and stable. Conditions under which efficiency loss may be bounded are presented, and the results are extended to the cases of general overlay networks and multiple autonomous systems. 1B1.4 Systems-Compatible Incentives, Dave Levin, Neil Spring, Bobby Bhattacharjee Selfish participants in a distributed system attempt to gain from the system without regard to how their actions may affect others. To maintain desirable system-wide properties in the presence of selfish users, designers are increasingly turning to the powerful mechanisms offered by economics and game theory. Combining the two fields of economics and systems design

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introduces new challenges of achieving incentive compatibility in systems we can deploy in today’s Internet. In this paper, we explore the interactions between systems and the mechanisms that give users incentives to cooperate. Using findings from recent work on incentive-compatible systems, we discuss several economic mechanisms and assumptions: money, punishment, and altruism. We seek to understand when these mechanisms violate system properties. Among the potential pitfalls we present is a phenomenon we call the price of altruism: altruistic peers can impose a loss of social good in some systems. We also discuss systems-compatible mechanisms that have been used in real, distributed systems, and attempt to extract the underlying design principles that have led to their success.

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1B2 Power Control II 14:00-15:30 Chair: Gürdal Arslan

1B2.1 From Competition to Coopetition: Stackelberg Equilibrium in Multi-user Power Control Games, Yi Su, Mihaela van der Schaar This paper considers the problem of how to allocate power among competing users sharing a frequency- selective interference channel. We model the interaction between these selfish users as a non-cooperative game. We study how a foresighted user, who knows the channel state information and response strategies of its competing users, should optimize its own transmission strategy. To characterize this multiuser interaction, the Stackelberg equilibrium is introduced. We start by analyzing in detail a simple two-user scenario, where the foresighted user can determine its optimal transmission strategy by solving a bi-level program which allows him to account for the myopic user’s response strategies. Therefore, the competition among users is transformed into a cooperative competition (coopetition) since the foresighted user will avoid interfering the myopic user. Since the optimal solution is computationally prohibitive, we propose a low-complexity algorithm based on Lagrangian duality theory. Numerical simulations illustrate that, if a foresighted user has the necessary information about its competitor, the resulting coopetition will benefit both users. Possible methods to acquire the required information and to extend the formulation to more than two users are also discussed. 1B2.2 A Power Allocation Strategy using Game Theory in Cognitive Radio Networks, Enrico Del Re, Gherardo Gorni, Luca Simone Ronga, Rosalba Suffritti The Cognitive Radio approach can be considered as a promising and suitable solution to solve in an efficient and flexible way the increasing and continuous demand of services and radio resources. This paper investigates how the adoption of a cognitive radio strategy can help in the coexistence problem of two wireless networks operating on the same spectrum of

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frequencies. A DVB-SH based satellite network will be considered as primary system, while an infrastructured wireless terrestrial network will constitute the cognitive radio based secondary system. In this work it will be presented a power resource allocation technique based on Game Theory, considering mainly Potential Games. We will show the proposed approach is suitable for distributed implementation, furthermore it provides performances comparable to an heuristic allocation method representing the optimum allocation. The comparison between these two resource allocation methods will be provided as result of this work.

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1B2.3 Stochastic Games with One-Step Delay Sharing Information Pattern with Application to Power Control, Eitan Altman, Vijay Kamble, Alonso Silva Non-cooperative game theory has gained much interest as a paradigm for decentralized control in communication networks. It allows to get rid of the need for a centralized controller. Decentralizing the decision making may result in situations where agents (decision makers) do not have the same view of the network: the information available to agents vary from one agent to another. The global view of the network state cannot be available to an agent as fast as the information on its local state. Incorporating into the decentralized control paradigm this information asymmetry renders it applicable to a much wider class of situations. In this paper we model the above information asymmetry using the one-step delay sharing information pattern from team theory and generalize it to the context of non-cooperative games. We study its properties and apply it to distributed power control problem. 1B2.4 MAC Games for Distributed Wireless Network Security with Incomplete Information of Selfish and Malicious User Types, Yalın Sağduyu, Randall Berry, Anthony Ephremides We consider game theoretic models of wireless medium access control (MAC) in which each transmitter makes individual decisions regarding their power level or transmission probability. This allows for scalable distributed operation; however, it can also enable users to pursue malicious objectives such as jamming other nodes to deny them service. We study games with two types of players: selfish and malicious transmitters. Each type is characterized by a utility function depending on throughput reward and energy cost. Furthermore, we focus on the setting where the transmitters have incomplete information regarding other transmitters’ types, modeled as probabilistic beliefs. We first analyze a power-controlled MAC game in which the nodes select powers for continuous transmissions and then extend this to a random access MAC in which nodes choose transmission probabilities. For each case, the Bayesian Nash equilibrium strategies are derived for different degrees of uncertainty, and the resulting equilibrium throughput of selfish nodes is characterized. We identify conditions in which the throughput improves with increasing type uncertainty and introduce

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Bayesian learning mechanisms to update the type beliefs in repeated games. For unknown types and costs, we also specify the equilibrium cut-off thresholds for monotonic transmission decisions. The analysis provides insights into the optimal defense mechanisms against denial of service attacks at the MAC layer in wireless networks. 1B3 Equilibrium Analysis 14:00-15:30 Chair: Lacra Pavel

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1B3.1 Mean Field Asymptotic of Markov Decision Evolutionary Games, Hamidou Tembine, Jean Yves Le Boudec, Rachid El Azouzi, Eitan Altman We introduce Markov Decision Evolutionary Games with N players, in which each individual in a large population interacts with other randomly selected players. The states and actions of each player in an interaction together determine the instantaneous payoff for all involved players. They also determine the transition probabilities to move to the next state. Each individual wishes to maximize the total expected discounted payoff over an infinite horizon. We provide a rigorous derivation of the asymptotic behavior of this system as the size of the population grows to infinity. We show that under any Markov strategy, the random process consisting of one specific player and the remaining population converges weakly to a jump process driven by the solution of a system of differential equations. We characterize the solutions to the team and to the game problems at the limit of infinite population and use these to construct almost optimal strategies for the case of a finite, but large, number of players. We show that the large population asymptotic of the microscopic model is equivalent to a (macroscopic) Markov decision evolutionary game in which a local interaction is described by a single player against a population profile. We illustrate our model to derive the equations for a dynamic evolutionary Hawk and Dove game with energy level. 1B3.2 Job Market Signaling Equilibria with Unobserved Cost Functions and Higher Education Reforms, Giuseppe Rose In this paper we argue that if firms cannot observe the individuals’ cost of acquiring education, inefficient pooling equilibria consistent with forward induction may characterize the job market signaling game. Continuous changes in the educational system may affect agents’ beliefs generating pooling equilibria consistent with forward reasoning. The welfare comparisons between separating and pooling equilibria should prevent governments to implement too often policies that deeply modify the educational system without a serious long run perspective. The role that European Union’ directives may have in addressing long run reforms could be fundamental in order to modernize higher education and to avoid the effects of reforms based on ungrounded political conveniences.

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1B3.3 How to Find Nash Equilibria with Extreme Total Latency in Network Congestion Games?, Heike Sperber We study the complexity of finding extreme pure Nash equilibria in symmetric network congestion games and analyse how it depends on the graph topology and the number of users. In our context best and worst equilibria are those with minimum respectively maximum total latency. We establish that both problems can be solved by a Greedy algorithm with a suitable tie breaking rule on parallel links. On series-parallel graphs finding a worst Nash equilibrium is NP-hard for two or more users while finding a best one is solvable in polynomial time for two users and NP-hard for three or more. Additionally we establish NP-hardness in the strong sense for the problem of finding a worst Nash equilibrium on a general acyclic graph.

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1B3.4 Nash Equilibrium Design and Optimization, Tansu Alpcan, Lacra Pavel The general problem of Nash equilibrium design is investigated from an optimization perspective. Within this context, a specific but fairly broad class of noncooperative games are considered that have been applied to a variety of settings including network congestion control, wireless uplink power control, and optical power control. The Nash equilibrium design problem is analyzed under various knowledge assumptions (full versus limited information) and design objectives (QoS versus utility maximization). Among other results, the “price of anarchy” is shown not to be an inherent feature of games that incorporate pricing mechanisms, but merely a misconception that often stems from arbitrary choice of game parameters. Moreover, a simple linear pricing is sufficient for design of Nash equilibrium according to a chosen global objective for a general class of games and under suitable information assumptions 1C1 Spectrum Sharing I 16:00-17:30 Chair: Randy Berry 1C1.1 Congestion Games with Resource Reuse and Applications in Spectrum Sharing, Mingyan Liu, Sahand Haji Ali Ahmad, Yunnan Wu In this paper we consider an extension to the classical definition of congestion games (CG) in which multiple users share the same set of resources and their payoff for using any resource is a function of the total number of users sharing it. The classical congestion games enjoy some very appealing properties, including the existence of a Nash equilibrium and that every improvement path is finite and leads to such a NE (also called the finite improvement property or FIP), which is also a local optimum to a potential function. On the other hand, this class of games does not model well the congestion or resource sharing in a wireless context, a prominent feature of which is spatial reuse. What this translates to in the context of a

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congestion game is that a user’s payoff for using a resource (interpreted as a channel) is a function of the its number of its interfering users sharing that channel, rather than the total number among all users. This makes the problem quite different. We will call this the congestion game with resource reuse (CG-RR). In this paper we study intrinsic properties of such a game; in particular, we seek to address under what conditions on the underlying network this game possesses the FIP or NE. We also discuss the implications of these results when applied to wireless spectrum sharing.

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Sarkar, Chandramani Singh Efficacy of proliferation of commercial wireless networks can be substantially enhanced through large scale cooperation among different providers. If a group of providers cooperate by allowing customers to be served by the resources of the whole group rather than just those of their own providers, they have the potential to utilize their resources more efficiently and enhance the quality of service they can offer. This in turn can result in higher profits for the providers. Such cooperation can, however, be successfully implemented if providers in a coalition judiciously allocate the resources, such as spectrum and base stations, accesspoints, etc., in a way that the individuals payoffs are commensurate to the resources they offer to the coalition. Initially, we assume that providers do not share their payoffs. We formulate this problem as a nontransferable payoff coalitional game and show that there exists a cooperation strategy that leaves no incentive for any subset of providers to split from the grand coalition, i.e., the core is nonempty. To compute this cooperation strategy and the corresponding payoffs, we subsequently relate this game and its core to an exchange market setting, and its equilibrium which can be computed by several practically efficient algorithms. Next, we investigate cooperation in a scenario, where customers are also decision makers and decide which provider to subscribe to, based on whether there is cooperation. We then formulate a coalitional game in this setting and show that it has a nonempty core. Finally, we extend previous results to the cases, where individuals assume more general payoff sharing relations, and their benefits are modeled as ”vector payoff functions”, comprised of mixed transferable and nontransferable components. 1C1.3 Service Provider Competition and Pricing for Dynamic Spectrum Allocation, Joydeep Acharya, Roy Yates We consider dynamic spectrum allocation in the downlink between multiple service providers and users, and develop a model that is applicable for many future scenarios. The service providers set prices for spectrum and transmit data to users, who purchase their spectrum. Each provider transmits at a specific power spectral density which is an indicator of the efficiency of the modulation and coding technology used for transmission. A user application is characterized by a utility function of its received rate which is

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a function of the allocated spectrum, its link gains to the providers and the providers’ transmit power spectral densities. The providers satisfy the spectrum requests of the users by purchasing spectrum from a broker. The providers compete to secure the services of the users and to maximize their profits. Using concepts from microeconomics, we characterize the SP price competition game and show that in the optimal solution each provider has its own customer base. We also characterize the prices charged and profits made by the providers and show how they vary with provider efficiencies and spectrum costs charged by the broker.

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1C1.4 On the Efficiency of Sequential Auctions for Spectrum Sharing, Junjik Bae, Eyal Beigman, Randall Berry, Michael Honig, Rakesh Vohra In previous work we have studied the use of sequential second price auctions for sharing a wireless resource, such as bandwidth or power. The resource is assumed to be managed by a spectrum broker (auctioneer), who collects bids and allocates discrete units of the resource. It is well known that a second price auction for a single indivisible good has an efficient dominant strategy equilibrium; this is no longer the case when multiple units of a homogeneous good are sold in repeated iterations. Previous work attempted to bound this inefficiency loss for two users with non-increasing marginal valuations and full information. This work was based on studying a setting in which one agent’s valuation for each resource unit is strictly larger than any of the other agent’s valuations and assuming a certain property of the price paid by such a dominant user in any sub-game. Using this assumption it was shown that the worst-case efficiency loss was no more than e-1. However, here we show that this assumption is not satisfied for all non-increasing marginals with this dominance property. In spite of this, we show that it is always true for the worst-case marginals for any number of goods and so the worst case efficiency loss for any non-increasing marginal valuations is still bounded by e-1. 1C2 Random Access Games 16:00-17:30 Chair: Yezekeal Hayel 1C2.1 Achieving Coordination in Random Access Networks Without Explicit Message Passing, Jaeok Park, Mihaela van der Schaar We propose a class of medium access control (MAC) protocols that utilize users’ own transmission decisions and feedback information from the past slots. We consider an idealized slotted Aloha system and formulate the problem of a protocol designer who cares about the total throughput, the short-term fairness, and the complexity of protocols. A solution to the protocol designer’s problem is provided with two users, and an approximate solution with three or more users. We use numerical methods to obtain optimal protocols that solve the protocol designer’s problem, compare the

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total throughput of optimal protocols with that of other protocols proposed in the literature, and analyze a trade-off between throughput and fairness. The results show that by utilizing information obtained in the previous slot, users can achieve some degree of coordination without explicit message passing, which leads to high total throughput. 1C2.2 Correlated Evolutionarily Stable Strategies in Random Medium Access Control, Hamidou Tembine, Eitan Altman, Rachid El-Azouzi, Yezekael Hayel

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networks with random number of users. We apply evolutionary game theoretic analysis to solve several problems: (a) We address the stability of Aloha-like systems with finitely many power levels. Specifically, we consider very large number of receivers distributed in several locations. Each of them receives packets from random number of users accessing the resource using Aloha-like algorithms. We provide an explicit expression for equilibria, correlated evolutionarily stable strategies, and prove some asymptotic stability results. (b) We apply correlation mechanism and evaluate the performance of random medium access when saturated users interact through interference. We introduce the benefit of correlation (BoC) to measure the gap between the probability of success at correlated evolutionarily stable strategies and the worst probability of success of evolutionarily stable strategies. We show that if only two power levels are available, the correlation mechanism reduces considerably the interference and the number of collisions. Moreover, the correlation mechanism is stable in long-term under several classes of bio-inspired evolutionary game dynamics. (c) Surprisingly, when the number of strategies is at least three, the correlation mechanisms do not improve the probability of success. 1C2.3 A Hierarchical Slotted Aloha Game, Essaid Sabir, Rachid El-Azouzi, Yezekael Hayel We consider in this paper a wireless system composed of one central receiver and several selfish transmitters communicating via the slotted aloha protocol. We study a noncooperative hierarchical system based on the Stackelberg game concept. Each user of our game tends to maximize his own throughput or minimize his expected delay of backlogged packets depending on his transmission probability and transmission probabilities of other users in the network. Using a 4D Markovian model, we compute the steady state of the system and derive the average throughput and expected delay. We then investigate the impact of introducing hierarchy in the random access protocol. Later, exhaustive performance evaluations were carried out, we show that the global performance of the system is improved compared to slotted aloha system without hierarchy. However, a not sharp performances slow-down may be observed for the followers when the number of users is not large, but they turn to outperform Nash equilibrium under average and heavy load.

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1C3 Wireless Networks I 16:00-17:30 Chair: Walid Saad 1C3.1 On Achieving Group Strategyproof Information Dissemination in Wireless Networks, Ajay Gopinathan, Zongpeng Li, Baochun Li We study the dissemination of common information from a source to multiple peers within a multihop wireless network, where peers are equipped with uniform omni-directional antennas and have a fixed cost per packet transmission. While many peers may be interested in the dissemination service, their valuation or utility for such a service is usually private information. A desirable routing and charging mechanism encourages truthful utility reports from the peers. We provide both negative and positive results towards such mechanism design. We show that in order to achieve the group strategyproof property, a compromise in routing optimality or budget-balance is inevitable. In particular, the fraction of optimal routing cost that can be recovered through peer charges cannot be significantly higher than 1/2. To answer the question whether constant-ratio cost recovery is possible, we further apply a primal-dual schema to simultaneously build a routing solution and a cost sharing scheme, and prove that the resulting mechanism is group strategyproof and guarantees 1/8 -approximate cost recovery against an optimal routing scheme.

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1C3.2 Conjecture-Based Channel Selection Game for Delay-Sensitive Users in Multi-Channel Wireless Networks, Hsien-Po Shiang, Mihaela van der Schaar In this paper, we study the problem of multi-user channel selection in multi-channel wireless networks. Specifically, we study the case in which the autonomous users deploy delay-sensitive applications. Existing centralized approaches result in efficient allocations, but require intensive message exchanges among the users (i.e. they are not informationally efficient). Current distributed approaches do not require any message exchange for collaboration, but they often result in inefficient allocations, because users only respond to their experienced contention in the network. Alternatively, in this paper we study a distributed channel selection approach, which does not require any message exchanges, and which leads to a system-wise Pareto optimal solution by enabling a foresighted user to predict the implications (based on their beliefs) of their channel selection on their expected future delays and thereby, foresightedly influence the resulting multi-user interaction. We model the multi-user interaction as a channel selection game and show how users can play an ε-consistent conjectural equilibrium by building near-accurate beliefs and competing for the remaining capacities of the channels. We analytically show that when the system has the foresighted user, this selfinterested leader can deploy a linear belief function in each channel and manipulates the equilibrium to approach the Stackelberg equilibrium. Alternatively, when the leader is

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altruistic, the system will converge to the system-wise Pareto optimal solution. We propose a low-complexity learning method based on linear regression for the foresighted user to learn its belief functions. 1C3.3 Widely-Linear Filtering and Non-Cooperative Transceiver Optimization in Wireless Data Networks, Stefano Buzzi, H. Vincent Poor, Alessio Zappone The issue of non-cooperative transceiver optimization in the uplink of a multiuser wireless data network with widely linear detection at the receiver is considered in this paper. While previous work in this area has focused on a simple real signal model, in this paper a baseband complex representation of the data is used, so as to properly take into account the I and Q components of the received signal. For the case in which the received signal is improper, a widely-linear reception structure, processing separately the data and their complex conjugates, is considered. The convergence of the well-known minimum mean square error (MMSE) iteration for spreading code adaptation is studied for the case in which widely-linear detection is used at the receiver. Interestingly, it is also found that spreading code optimization coupled with widely-linear filtering permits supporting, with no multiuser interference, a number of users that is twice the processing gain. Numerical results corroborate the validity of the theoretical analysis, and show that exploiting the improper nature of the data in non-cooperative resource allocation brings remarkable performance improvements in multiuser wireless systems.

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1C3.4 A Selfish Approach to Coalition Formation Among Unmanned Aerial Vehicles in Wireless Networks, Walid Saad, Zhu Han, Tamer Başar, Merouane Debbah, Are Hjørungnes Autonomous agents such as unmanned aerial vehicles (UAVs) have a great potential for deployment in next generation wireless networks. While current literature has been mainly focused on the use of UAVs for connectivity enhancement and routing in military ad hoc networks, this paper proposes a novel usage model for UAVs in wireless communication networks. In the proposed model, a number of UAVs are required to collect data from a number of randomly located tasks and transmit this data wirelessly to a common receiver (such as the central command). Each task represents a queue of packets that require collection and transmission to the central receiver. This problem is modeled as a hedonic coalition formation game between the UAVs and the tasks that interact in order to form disjoint coalitions. Each formed coalition is modeled as a polling system consisting of a number of UAVs, designated as collectors, which act as a single server that moves between the different tasks present in the coalition, collects and transmits the packets to a common receiver. Within each coalition, some UAVs might also take the role as a relay for improving the packet success rate of the transmission. The proposed coalition formation algorithm allows the tasks and the UAVs to take local selfish decisions to join or leave a

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coalition, based on the achieved benefit, in terms of effective throughput, and the cost in terms of delay. Simulation results show how the proposed algorithm allows the UAVs and tasks to self-organize into independent coalitions, while improving the performance, in terms of average player (UAV or task) payoff, of at least 30.26% relatively to a scheme that allocates nearby tasks equally among UAVs. 1C4 Game-Theoretic Analysis of Auctions and Network Security 16:00-17:30 Chair: Asuman Özdağlar

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1C4.1 Equilibria and Convergence of Auctions on Networks, Peng Jia, Peter E. Caines First, a quantized progressive second price auction mechanism called UQ-PSP is developed to allocate a divisible resource among arbitrary populations of agents. It is shown that (i) the states (i.e. bid prices and quantities) of the corresponding iterative dynamical auction system converge to a unique quantized (Nash) equilibrium with a common limit price for all agents, and (ii) the dynamics are independent of the initial data. Second, a network based auction is developed where each agent employs a UQ-PSP scheme by observing only their neighbors’ bids. The equilibria and convergence properties of this class of distributed auctions are established and are shown to depend on the network topology, and numerical examples are given. 1C4.2 Coexistence with Malicious Nodes: A Game Theoretic Approach, Wenjing Wang, Mainak Chatterjee, Kevin Kwiat In this paper, we use game theory to study the interactions between a malicious node and a regular node in wireless networks with unreliable channels. Since the malicious nodes do not reveal their identities to others, it is crucial for the regular nodes to detect them through monitoring and observation. We model the malicious node detection process as a Bayesian game with imperfect information and show that a mixed strategy perfect Bayesian Nash Equilibrium (also a sequential equilibrium) is attainable. While the equilibrium in the detection game ensures the identification of the malicious nodes, we argue that it might not be profitable to isolate the malicious nodes upon detection. As a matter of fact, malicious nodes and regular nodes can co-exist as long as the destruction they bring is less than the contribution they make. To show how we can utilize the malicious nodes, a post-detection game between the malicious and regular nodes is formalized. Solution to this game shows the existence of a subgame perfect Nash Equilibrium and the conditions that achieve the equilibrium. Simulation results and their discussions are also provided to illustrate the properties of the derived equilibria.

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1C4.3 Physical Layer Security Game: How to Date a Girl with Her Boyfriend on the Same Table, Zhu Han, Ninoslav Marina, Merouane Debbah, Are Hjørungnes Physical layer security is an emerging security concept that achieves perfect secrecy data transmission between the intended network nodes, while the eavesdropping malicious nodes obtain zero information. The so-called secrecy capacity can be improved using friendly jammers that introduce extra interference to the eavesdropping malicious nodes while the interference to the intended destination is limited. In this paper, we investigate the interaction between the source that transmits the desired data and friendly jammers who assist the source by “disguising” the eavesdropper. In order to obtain a distributed solution, we introduce a game theoretic approach. The game is defined in such a way that the source pays the friendly jammers to interfere the eavesdropper, and, therefore, increasing its secrecy capacity. Friendly jammers charge the source with a certain price for this “jamming servise”. There is a tradeoff for the price: If the price is too low, the profit of the jammers is low; and if the price is too high, the source would not buy the “service” (jamming power) or would buy it from other jammers. To analyze the game outcome, we define and investigate a Stackelberg game and construct a distributed algorithm. Our analysis and simulation results show the effectiveness of friendly jamming and the tradeoff for setting the price. The fancy title comes from the fact that it is similar to a scenario where the main fellow character (the source) tries to send a dating message to a lady (the intended destination), whose “poor” boyfriend plays the role of the eavesdropper that may hear the message. Friends of the source, the so-called “friendly jammers,” try to distract the boyfriend, so that the dating message can be secretly transmitted. The game is defined in order to derive what is the optimal price that the friends can charge for this “friendly” action.

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1C4.4 Secure Communication: A Mechanism Design Approach, Ludovic Renou, Tristan Tomala This paper considers a mechanism design model where a designer, or receiver, takes an action based on the information received by multiple players, or senders. The agents, senders and receiver, communicate in a fixed directed network. We characterize the communication networks for which, in any environment (utilities and beliefs) with a worst action, every incentive compatible social choice function is implementable on the network. We show that this holds true if and only if the network is weakly 2-connected. A network is weakly 2-connected if for each player i, who is not directly connected to the designer, there exists a player k and two vertex-disjoint paths from k to the designer such that i lies on one of the two paths. We couple encryption techniques together with appropriate incentives to secure the transmission of each player’s private information to the designer.

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2A1.1 Bidding Efficiently in Repeated Auctions with Entry and Observation Costs, Amir Danak, Shie Mannor

This paper introduces an efficient bidding strategy for budget-constrained buyers in repeated auctions with entry fees. We present a general algorithm that is applicable to distributed resource allocation. The game is modeled on an economically reasonable assumption [1] according to which any player can participate in an auction after paying for information about the value of the auctioned item, and for the preparation of his bid. We address learning by each bidder of an optimal participation strategy for spending his budget profitably, based on the history of his successes and failures in past transactions. Players’ transient and long-term attitudes are illustrated in a symmetric Bayesian equilibrium of a market-based network resource allocation problem. 2A1.2 Learning in the Presence of Noise, Panayotis Mertikopoulos, Aris Moustakas

We investigate the emergence of rationality in repeated games where, at each iteration, the players’ payoffs are randombly perturbed (to account e.g. for the effects of fading or errors in the reading of one’s throughput). We see that even if players start out completely uneducated about the game, there is a simple learning scheme that enables them to eventually weed out the noise and identify suboptimal choices, regardless of the noise level. More precisely, we show that strategies that are strictly dominated (even iteratively) become extinct in the long run, i.e. players exhibit rational behavior. As an application, we model a number of users that are able to switch dynamically between multiple wireless nodes and see that they are able to pick up which node works best for them, even in the presence of high performance fluctuations. 2A1.3 Online Learning in Markov Decision Processes with Arbitrarily Changing Rewards and Transitions, Jia Yuan Yu, Shie Mannor We consider decision-making problems in Markov decision processes where both the rewards and the transition probabilities vary in an arbitrary (e.g., non-stationary) fashion. We present algorithms that combine online learning and robust control, and establish guarantees on their performance evaluated in retrospect against alternative policies—i.e., their regret. These guarantees depend critically on the range of uncertainty in the transition probabilities, but hold regardless of the changes in rewards and transition probabilities over time. We present a version of the main algorithm in the setting where the decision-maker’s observations are limited to its trajectory,

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and another version that allows a trade-off between performance and computational complexity. 2A1.3 Deterministic Approximation of Stochastic Evolutionary Dynamics, Robert Molzon Deterministic dynamical systems are often used in economic models to approximate stochastic systems with large numbers of agents. A number of papers have provided conditions that guarantee that the deterministic models are in fact good approximations to the stochastic models. Much of this work has concentrated on the continuous time case with systems of differential equations approximating discrete time stochastic systems, although some important early work in this field considered discrete time approximations. A crucial aspect of the existing work is the assumption that the stochastic models involve agents of finitely many types. However, many existing economic models assume agent types may take on infinitely many distinct values. For example, some models assume agents hold divisible amounts of money or goods, and therefore agent types form a continuum. In this paper we examine discrete time deterministic approximations of stochastic systems, and we allow agent attributes to be described by infinitely many types. If the set of types that describe agents is a continuum, then individuals, in some sense, are unique, and it is not obvious that the stochastic models that rely on random matching of agents as the source of uncertainty can be approximated in a deterministic manner. Indeed, we give two examples that show why a law of large numbers may not lead to deterministic approximations. In the positive direction, we provide conditions that allow for good deterministic approximations even in the case of a continuum of types.

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2A2 Evolutionary Games 11:15-12:45 Chair: Pierre Bernhard

2A2.1 Virulence Evolution Trough a Latency-Transmission Trade-Off: Implications as to the Durability of Resistance in Agriculture, Frederic Hamelin

In evolutionary epidemiology, most of the existing models address virulence evolution through a transmission-virulence trade-off. Although some models consider a coupling with other host-parasite interaction features such as clearance, there seem to be no model considering a coupling with a trait which is however often measured, and may have some life-historical significance: the latent period. In this note, we use a simple model that explicitly incorporates the latent period to gain some insight into the virulence evolution determinants. We discuss the model’s implications as to the durability of resistance in agriculture. In particular, we show that an anti-growth-rate resistance may, contrarily to the classical insight, lower intrinsic

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virulence. This is because latency, as an additional “degree of freedom”, may absorb what would otherwise result in an virulence increase towards less resistant hosts. Moreover, this goes with a greater healthy host density, regardless whether the crop is resistant or not, thanks to maladaptation. 2A2.2 Strategy Dependent Mortality in Life History Games, David Ramsey

In games such as the war of attrition and parental care games the length of time spent in a realisation of the game is dependent on the strategy used. Hence, there is a trade off between the mean reward obtained per realisation of the game and the mean number of games played per unit time. Such a game should not be modelled using the standard two player form, but should be defined as a game against the field (a large population game). In parental care games, such an approach also enables us to define a more consistent model, which takes into account, for example, the obvious fact that each individual has one parent of both sexes and that the ease with which a male deserter can find a new partner depends on the strategy profile used in the population. If the mortality rate is independent of strategy, then each individual should simply maximise the rate of producing offspring. However, if mortality rates depend on strategy, then at equilibrium an individual should maximise the number of offspring produced during their lifetime. This paper considers pure equilibria in a parental care game, in which the mortality rate depends on an individual’s strategy.

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2A2.3 Games on Graphs that Grow Deterministically, Richard Southwell, Chris Cannings

We introduce an adaptive graph model where strategy assigned vertices reproduce themselves (having offspring with the same neighbourhood) and unfit vertices get removed. We study how different games cause different graphs to evolve. Under some games graphs grow and break into self replicating structures. Small initial graphs can lead to the generation of vast ‘ecosystems’ containing thousands of kinds of structures that change and make copies of one another. Understanding how local interactions induce self replication is important to biology. We examine self replicative processes under various games. We investigate how resilient these processes are to stochasticity and we introduce several modified growth models where analysis of the dynamics is easier. We introduce an adaptive graph model where strategy assigned vertices reproduce themselves (having offspring with the same neighbourhood) and unfit vertices get removed. We study how different games cause different graphs to evolve. Under some games graphs grow and break into self replicating structures. Small initial graphs can lead to the generation of vast ‘ecosystems’ containing thousands of kinds of structures that change and make copies of one another. Understanding how local interactions induce self replication is important to biology. We examine self replicative processes under various games. We

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investigate how resilient these processes are to stochasticity and we introduce several modified growth models where analysis of the dynamics is easier. 2A2.3 Competition Between Foraging Predators and Hiding Preys as a Nonzero-Sum Differential Game, Andrei Akhmetzhanov, Pierre Bernhard, Frédéric Grognard, Ludovic Mailleret In this work we investigate a (seasonal) preypredator model where the system evolves during a season whose length is fixed. Predators have the choice between foraging the food (eating preys) and reproducing (laying eggs at a rate proportional to their energy). Preys can either eat, which would maintain their population in the absence of predators, or hide from the predators but they then suffer a positive mortality rate. In this case the population size can decrease even faster than if they were not hiding and were foraged by the predators. In their own turn they lay eggs at a constant rate whether they are hiding or eating. Following Darwin’s principle that the fittest population will survive we postulate that both populations must maximize the number of their offspring, which yields a nonzerosum differential game.

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2A3 Game Theoretic Network Models II 11:15-12:45 Chair: Rahul Jain

2A3.1 A Tight Characterization Of Strategic Games With A Unique Equlibrium, Antoniy Ganchev, Lata Narayanan, Sunil Shende Media access protocols in wireless networks require each contending node to wait for a backoff time chosen randomly from a fixed range, before attempting to transmit on a shared channel. However, nodes acting in their own selfish interest may not follow the protocol. In this paper, we use a game-theoretic approach to study how nodes might be induced to adhere to the protocol. In particular, a static version of the problem is modeled as a strategic game played by noncooperating, rational players (the nodes). A strategy for a player corresponds to a backoff value in the medium access protocol. We are interested in designing a game which exhibits a unique Nash equilibrium corresponding to a pre-specified full-support distribution profile. In the context of the media access problem, the equilibrium of the game would correspond to nodes following the protocol, viz. choosing backoff times randomly from a given range of values according to the pre-specified distribution. Building on results described in earlier work, we identify the exact relationship that must hold between the cardinalities of the players’ action sets that would make it possible to design such a game.

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2A3.2 Combinatorial Agency with Audits, Raphael Eidenbenz, Stefan Schmid This paper studies the question of how to overcome inefficiencies due to hidden actions in a rational milieu, such as a grid computing system with open clientele. We consider the so-called principal-agent model known from economic theory, where the members (or agents) of a distributed system collaborate in complex ways. We adopt the perspective of the principal and investigate auditing mechanisms that incentivize participants to contribute more to a common project. As conducting audits might be costly, the principal must balance the tradeoff between low auditing costs and the level of incentives offered to the participants to exert high effort. We present optimal solutions for this optimization problem in scenarios, where the project success either depends on all, on any or on the majority of the participants succeeding in their subtask. In the first case, we further find that with an increasing principal valuation, there is exactly one transition point where the optimal choices for achieving the maximal principal utility switch. Compared to a combinatorial agency without the leverage of audits, this transition occurs earlier.

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2A3.3 A Game-Theoretical Approach to Incentive Design in Collaborative Intrusion Detection Networks, Quanyan Zhu, Carol Fung, Raouf Boutaba, Tamer Başar Traditional intrusion detection systems (IDSs) work in isolation and may be easily compromised by new threats. An intrusion detection network (IDN) is a collaborative IDS network intended to overcome this weakness by allowing IDS peers to share collective knowledge and experience, hence improve the overall accuracy of intrusion assessment. In this work, we design an incentive model based on trust management by using game theory for peers to collaborate truthfully without free-riding in an IDN environment. We show the existence and uniqueness of a Nash equilibrium under which peers can communicate in an incentive compatible manner. Using duality of the problem, we develop an iterative algorithm that converges geometrically to the equilibrium. Our numerical experiments and discrete event simulation demonstrate the convergence to the Nash equilibrium and the incentives of the resource allocation design. 2A3.4 Efficiency and Stability of Nash Equilibria in Resource Allocation Games, Tobias Harks, Konstantin Miller We study resource allocation games, where users send data along paths and links in the network charge a price equal to marginal cost. When users are price taking, it is known that there exist distributed dynamics that converge towards a fully efficient Nash equilibrium. When users are price anticipating, however, a Nash equilibrium does not maximize total utility in general. In this paper, we explore the inefficiency of Nash equilibria for general networks and semi-convex marginal cost functions. While it is known

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that for m ≥ 2 users and convex marginal cost functions, no efficiency guarantee is possible, we prove that an additional differentiability assumption on marginal cost functions implies a bounded efficiency loss of 2/(2m + 1). For polynomial marginal cost functions with nonnegative coefficients, we precisely characterize the price of anarchy. We also prove that the efficiency of Nash equilibria significantly improves if all users have the same strategy space and the same utility function. We propose a class of distributed dynamics and prove that whenever a game admits a potential function, these Dynamics globally converge to a Nash equilibrium. Finally, we show that in general the only class of marginal cost functions that guarantees the existence of a potential function are affine linear functions.

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3A1 Stochastic Games 11:15-12:45 Chair: Peter Caines

3A1.1 A Constrained Evolutionary Gaussian Multiple Access Channel Game, Quanyan Zhu, Hamidou Tembine, Tamer Başar In this paper, we formulate an evolutionary multiple access channel game with continuous-variable actions and coupled rate constraints. We characterize Nash equilibria of the game and show that the pure Nash equilibria are Pareto optimal and also resilient to deviations by coalitions of any size, i.e., they are strong equilibria. We use the concepts of price of anarchy and strong price of anarchy to study the performance of the system. The paper also addresses how to select one specific equilibrium solution using the concepts of normalized equilibrium and evolutionary stable strategies. We examine the long-run behavior of these strategies under several classes of evolutionary game dynamics such as Brownvon Neumann-Nash dynamics, and replicator dynamics. 3A1.2 Communication Complexity of Stochastic Games, Nagarajan Krishnamurthy, T. Parthasarathy, G. Ravindran

We derive upper and lower bounds on the communication complexity of determining the existence of pure strategy Nash equilibria for some classes of stochastic games. We prove that pure equilibria of single controller stochastic games and those of SER-SIT (Separable Reward – State Independent Transition) games correspond to those of bimatrix games that are constructed from these stochastic games. Hence we extend communication complexity upper bounds of bimatrix games to these stochastic games. For SER-SIT games, we prove an upper bound of O(n2) which is tight and which coincides with that for bimatrix games. Here n is the number of actions of each player in each state. Note that this bound is independent of the size of the actual payoffs. For singlecontroller games, we obtain an upper bound of min (O(n2|S|), O(|S| n2 log M)) where S is the set of states and M is the largest entry across all payoff matrices. Further, we reduce bimatrix games to stochastic games and hence, the lower bound extends from bimatrix games to stochastic games as well. We also establish the following results while proving upper bounds for SER-SIT games. To prove that pure equilibria of SER-SIT games correspond to those of auxiliary bimatrix games, we show that every SER-SIT game that has a pure equilibrium has a state-independent pure equilibrium too. We also show that we cannot relax the constraints of separable rewards or state independent transitions. We provide counter examples when the game is SER (but not SIT) and SIT (but not SER).

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3A1.3 Large Population Games in Radial Loss Networks: Computationally Tractable Equilibria for Distributed Network Admission Control, Zhongjing Ma, Peter Caines, Roland Malhamé The computational intractability of the dynamic programming (DP) equations associated with optimal admission and routing in stochastic loss networks of any non-trivial size (Ma et al, 2006, 2008) leads one to consider suboptimal distributed game theoretic formulations of the problem. The special class of radial networks with a central core of infinite capacity is considered, and it is shown (under adequate assumptions) that an associated distributed admission control problem becomes tractable asymptotically, as the size of radial network grows to infinity. This is achieved by following a methodology first explored by M. Huang et. al. (2003, 2006-2008) in the context of large scale dynamic games for sets of weakly coupled linear stochastic control systems. At the established Nash equilibrium, each agent reacts optimally with respect to the average trajectory of the mass of all other agents; this trajectory is approximated by a deterministic infinite population limit (associated with the mean field or ensemble statistics of the random agents) which is the solution of a particular fixed point problem. This framework has connections with the mean field models studied by Lasry and Lions (2006, 2007) and close connections with the notion of oblivious equilibrium proposed by Weintraub, Benkard, and Van Roy (2005, 2008) via a mean field approximation. 3A2 Wireless Networks II 11:15-12:45 Chair: Daniel Palomar

3A2.1 Power Control Game in Protected and Shared Bands: Manipulability of Nash Equilibrium, Eduard Jorswieck, Rami Mochaourab

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We consider a downlink resource allocation problem for two systems or cells each consisting of a base station and multiple mobile stations. Each cell operates on a protected band for exclusive use and a band shared with the other cell. On simultaneous transmission in the shared band, the two systems disturb one another with interference. The strategies of the systems are their choices of power allocations in their two bands with regard to individual sum power constraints. Here, the conflict present between the systems is best analyzed using game theory. In the first part, we study the static non-cooperative power control game with complete information. Existence and uniqueness of the Nash equilibrium are examined. Based on a suitable feedback model, we ask in the second part, whether the Nash equilibrium can be manipulated by reporting untruthful information within the system. The aim is to find suitable functions to suppress false feedback information from giving advantage to the dishonest system and degrading fairness between the systems. Here, we apply results from mechanism design to

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propose a modified expected payoff function at the mobile stations to force truthful feedback. 3A2.2 Deployment Analysis of Cooperative OFDM Base Stations, Gaoning He, Hamidou Tembine, Mérouane Debbah

We study the resource allocation problem in Orthogonal Frequency Division Multiplexing (OFDM) systems as a cooperative game. The goal is to maximize the overall system rate considering fairness metrics among users. We propose Nash bargaining solution (NBS) as a tool that achieves point(s) on the Pareto frontier of the game theoretical rate region under asymmetric conditions. Moreover, we provide a practical stochastic algorithm that can converge to one of the fairness points on the Pareto boundary. The numerical results show that the NBS not only maintains fair resource allocation for all users, but also provides a desirable spectral efficiency for the OFDM system. 3A2.3 Bargaining Over the Interference Channel with Total Power Costraints, Ephraim Zehavi, Amir Leshem

In this paper we study the computation of the Nash bargaining solution for the two players, K frequency bands case, under joint FDM/TDM spectrum allocations and total power constraint. The results improve previous analysis by Han et al. We provide a computationally efficient algorithm as well as detailed analysis of the Karush-Kuhn-Tucker (KKT) equations necessary for proving the correctness of the algorithm. Simulation results demonstrating the gain of the NBS over competitive approaches are also provided. 3A2.4 Competitive Optimization of Cognitive Radio MIMO Systems via Game Theory, Gesualdo Scutari, Daniel P. Palomar and Sergio Barbarossa

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The concept of cognitive radio (CR) has recently received great attention from the researchers’ community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper, we propose a distributed approach based on game theory to design cognitive MIMO transceiver in hierarchical CR networks, where primary users establish null and/or soft shaping constraints on the transmit covariance matrix of secondary users, so that the interference generated by secondary users be confined within the interference-temperature limits. We formulate the resource allocation problem among secondary users as a strategic noncooperative game, where each transmit/receive pair competes against the others to maximize the information rate over his own MIMO channel, under transmit power and/or null/soft shaping constraints. We provide a unified set of conditions that guarantee the uniqueness and global asymptotic stability of the Nash equilibrium of all the proposed games

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through totally distributed and asynchronous algorithms. Interestingly, the proposed algorithms overcome the main drawback of classical waterfilling based algorithms−the violation of the interference-temperature limits−and they have many of the desired features required for cognitive radio applications, such as low-complexity, distributed nature, robustness against missing or outdated updates of the users, and fast convergence behavior. 3A3 Pricing 11:15-12:45 Chair: Moshe Haviv

3A3.1 Fairer Pricing of Resource Allocation Strategies – Individual Guarantees Approach, Siddharth Naik, Holger Boche

We propose an individual guarantees approach for comparing resource allocation strategies at the physical layer in wireless systems. For this purpose we utilize the collective choice function to represent resource allocation strategies. We utilize an axiomatic framework to emulate certain desirable and undesirable properties of resource allocation strategies. We utilize basic bargaining sets as a tool to investigate the individual guarantees of certain commonly encountered resource allocation strategies – max-min balancing, maximization of the sum of utilities and proportional fairness. We also provide certain interesting consequences to continuity related properties of resource allocation strategies. The basic bargaining sets along with the individual guarantee structures provide certain intuition as to what could be means for implementing a fairer pricing strategy based on the losses incurred by users currently in the system, when new users arrive in the system. 3A3.2 Competition for Subscribers Between Mobile Operators Sharing a Limited Resource, Hélène Le Cadre, Mustapha Bouhtou, Bruno Tuffin

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Radio spectrum allocation is essential to the provision of mobile communication services. The spectrum is a finite resource and can accomodate a limited number of simultaneous users at one time. Due to this scarcity, allocating traditional mobile licenses to new mobile operators is unrealizable and new entrants should bargain access to the networks of the incumbents. In this article a Mobile Network operator (MNO) shares his finite network resource with a Mobile Virtual Network operator (MVNO) lacking the infrastructure. This latter has the opportunity to invest in advertising / content to compensate for her quality of service degradation. We introduce competition between both providers on consumers and prove that the associated three-level game has a unique Nash equilibrium in the retail prices. Besides the MNO should rather use a bundle based pricing approach while the MVNO would prefer linear pricing. Finally the introduction of file-sharing platforms offering free-downloadable programs might increase both providers’ revenues.

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3A3.3 Pricing Model for the Secondary Market Architecture in Cognitive Radio Networks, Gülfem Işıklar Alptekin, Ayşe Başar Bener

The traditional rigid spectrum allocation approach, which assigns fixed portions of spectrum to specific license holders for long term basis, is unable to manage the spectrum efficiently any longer. In order to fully utilize scarce spectrum resources in wireless networks, dynamic spectrum allocation becomes a promising approach. It is the cognitive radio technology that enables a dynamic spectrum access network sharing a wide range of available spectrum in an opportunistic manner. In this paper, we propose a pricing model for short-term sub-lease of unutilized spectrum bands to different service providers. We built our model on a competitive spectrum exchange marketplace. We obtain the equilibrium spectrum prices via a game theoretical pricing model. The Nash equilibrium point tells the spectrum holders the ideal price and quality of service level values where profit is maximized at the highest level of customer satisfaction. As the game model suggest, the numerical results show that the price and QoS level values of the network providers depend on the price and QoS of their own bands as well as the prices and QoS levels of their competitors’ bands. 3A3.4 Broadcasting Forever, Eitan Altman and Moshe Haviv In a pay-per-view scheme, a service provider multicasts the program for which it has the rights on demand only to those who have paid for it. However, once payments are made it is tempting to broadcast the program to all. This occurs both in order to increase advertising revenues (due to a higher rating) and due to the extra costs associated with multicasting in comparison with broadcasting. Of course, this can be done only once as reputation will then be lost. We describe a pricing mechanism which results in broadcasting while still causing those willing to pay, to do so and at the monopoly price.

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3B1 Spectrum Sharing II 14:00-15:30 Chair: Richard La 3B1.1 Computational Analysis of an Auction for Licensed and Unlicensed Use of Spectrum, William W. Sharkey, Fernando Beltrán, Mark Bykowsky

This paper employs simulation methods to evaluate the ability of three different auction mechanisms to determine an efficient license regime for radio spectrum as well as the efficient ownership of the associated rights. The two regimes explored are “licensed” spectrum, in which a winning

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bidder maintains exclusive rights to use the spectrum, subject only to technical restrictions, and “nonlicensed” spectrum, in which multiple users are able to share spectrum on an open access basis. For each auction, we examine bidder incentives and provide detailed reports on both auction revenue and bidder surplus in a set of Nash equilibrium outcomes. Results are consistent with the preliminary conclusions of Bykowsky et al. (2008), that a market can be used to allocate spectrum between licensed and unlicensed use. When there is a clear market preference for either licensed or unlicensed use, all three auction mechanisms arrive at efficient outcomes. However, in the absence of such a preference, a first-price auction appears to be the preferred mechanism. 3B1.2 Auction Mechanism for Spectrum Allocation and Profit Sharing, Sung Hyun Chun, Richard La

We examine the problem of designing an auction mechanism for dynamic spectrum sharing when there are multiple sellers and multiple buyers. First, we study the interaction among homogeneous buyers of spectrum as a noncooperative game and show the existence of a symmetric mixed-strategy Nash equilibrium (SMSNE). Second, we prove that there exists an incentive for risk neutral sellers of the spectrum to cooperate to maximize their expected profits at the SMSNEs of buyers’ noncooperative game. Finally, we model the interaction among the sellers as a cooperative game and demonstrate that the core of the cooperative game is nonempty. This indicates that there exists a way for the sellers to share the profits in a such manner that no subset of sellers will deviate from cooperating with the remaining sellers. 3B1.3 Evolution and Market Share of Wireless Community Networks, Mohammad Hossein Manshaei, Peter Marbach, Jean-Pierre Hubaux

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Wireless community networks that operate in the unlicensed spectrum have emerged as a low-cost alternative for providing high-speed wireless data services. By using WiFi access points that are provided and managed by community members, wireless community networks can offer high-speed data services at a much lower cost compared with traditional licensed band operators. However, depending on the number of members, the quality-of-service in terms of coverage and data rates provided by wireless community networks can be significantly lower compared with traditional licensed band operators. As a result, it is not clear whether wireless community networks will be able to capture a significant share of the market for wireless data services. In this paper we use a game-theoretic approach to model and study the evolution, and potential market share, of wireless community networks. We also study whether it is profitable for a licensed band provider to complement its licensed band data service with a low-cost service based on a wireless community network.

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3B1.4 Spectrum Sharing Games on the Interference Channel, Mehdi Bennis, Mael Le Treust, Samson Lasaulce, Merouane Debbah, Jorma Lilleberg

In this paper, we address the problem of spectrum sharing where competitive operators coexist in the same frequency band. First, we model this problem as a strategic non-cooperative game where operators simultaneously share the spectrum according to the Nash Equilibrium (N.E). Given a set of channel realizations, several Nash equilibria exist which renders the outcome of the game unpredictable. For this reason, the spectrum sharing problem is reformulated as a Stackelberg game where the first operator is already being deployed and the secondary operator follows next. The Stackelberg equilibrium (S.E) is reached where the best response of the secondary operator is taken into account upon maximizing the primary operator’s utility function. Finally, we assess the goodness of the proposed distributed approach by comparing its performance to the centralized approach. 3B2 Game Theoretic Network Models III 14:00-15:30 Chair: Rachid El Azouzi 3B2.1 Queueing Game Models for Differentiated Services, Parijat Dube, Rahul Jain,

We develop a framework to study differentiated services when there are competing network providers. We adopt a multi-class queueing model, where providers post prices for various service classes. Traffic is elastic and users are Quality of Service (QoS)-sensitive, and choose a queue and a class with one of the providers. We model the relationship between capacity, QoS and prices offered by service providers in a competitive network services market. We establish sufficient conditions for existence of Nash equilibrium in the multi-class queueing game. We also explore characterization of inefficiency in the multi-class queueing game model. The modeling framework we provide can be used to study important properties of the equilibrium solution which may be exploited to provide useful guidelines for performance planning and pricing strategies for firms competing in network resource markets.

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3B2.2 Nash Equilibrium Based Fairness, Hisao Kameda, Eitan Altman, Corinne Touati, Arnaud Legrand

There are several approaches of sharing resources among users. There is a noncooperative approach wherein each user strives to maximize its own utility. The most common optimality notion is then the Nash equilibrium. Nash equilibria are generally Pareto inefficient. On the other hand, we consider a

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Nash equilibrium to be fair as it is defined in a context of fair competition without coalitions (such as cartels and syndicates). We show a general framework of systems wherein there exists a Pareto optimal allocation that is Pareto superior to an inefficient Nash equilibrium. We consider this Pareto optimum to be ‘Nash equilibrium based fair.’ We further define a ‘Nash proportionately fair’ Pareto optimum. We then provide conditions for the existence of a Pareto-optimal allocation that is, truly or most closely, proportional to a Nash equilibrium. As examples that fit in the above framework, we consider noncooperative flow-control problems in communication networks, for which we show the conditions on the existence of Nash-proportionately fair Pareto optimal allocations. 3B2.3 Cooperation in Underwater Sensor Networks, Florent Garcin, Mohammad Hossein Manshaei, Jean-Pierre Hubaux

In underwater sensor networks (UWSNs), one of the main concerns is to reduce the energy consumption in order to maximize the lifetime. This work focuses on multiple sensor networks governed by different authorities. If the authorities are willing to cooperate by forwarding each others’ packets, the global lifetime could be increased. However, a selfish authority could exploit the others’ collaborative behaviors. To investigate this cooperation, we apply concepts such as evolutionary game theory. A first analysis of a simple model determines that cooperation underwater can emerge without incentives. Then, we explore with an extended model what influences cooperation and in which way. Finally, we demonstrate how a new authority can fine tune its strategy when deploying its UWSN.

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3B2.4 Games with Coupled Propagated Constraints in General Topology Optical Networks, Yan Pan, Lacra Pavel

We consider games with coupled utilities and constraints towards optimizing channel optical signal-to-noise ratio (OSNR) in optical networks with arbitrary topologies. By fully using the flexibility that channel powers are adjustable at optical switches, we partition the network into stages where each stage is a link. We formulate a partitioned Nash game composed of link Nash games where each link Nash game is played towards minimizing channel OSNR degradation across the link. By breaking quasi-closed loops and selecting one link as the start, links/games can be placed sequentially in a ladder-nested form. The partition is simple and scalable and leads to a three-level hierarchical algorithm towards computation of Nash equilibria.

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3B3 Wireless Networks III 14:00-15:30 Chair: Amir Leshem 3B3.1 A Prioritized MAC Game Framework for Event Reporting in Sensor Networks, Qiong Shi, Cristina Comaniciu, Prathima Agrawal

In this paper we propose a game theoretic framework for a new approach for MAC design with prioritized event reporting in sensor networks. The MAC priority classes are adaptively assigned based on accuracy of location information for individual sensor nodes, and on data correlation structure. We show that for the proposed MAC solution, the event reporting results in more accurate and faster localization of the event. 3B3.2 Wireless Mesh Networking Games, Arnab Das, Azin Neishaboori, George Kesidis

We address the coverage range extension of Wireless Mesh Networks (WMNs) by motivating traffic relaying by in-range network subscribers. Two different game models for non-cooperative users are discussed: a primary market model in which all in-range and out-of-range customers subscribe to one provider, and a primary-secondary market model in which some in-range customers are secondary providers and sell resources to out-of-range users. For the first market type, the relays may engage in packet-dropping for their own throughput gain, but we justify why this would likely not occur in the second market type. In both market models, we analyze the dynamics of the price charged by each provider and the traffic demanded by each subscriber. Additionally, we discuss possible options for underlying MAC protocols that are suitable for thegames in play. We use an ALOHA-based framework to study the dynamics of the primary market, and an OFDMA-based framework to study the dynamics of the primary-secondary market. Lastly, we provide a simulation study for each model. 3B3.3 Resource Allocation Games in Interference Relay Channels, Elena-Veronica Belmega, Brice Djeumou, Samson Lasaulce

In this paper we study a distributed network comprising an interference channel in parallel with an interference relay channel. Therefore each source node can use two frequency bands and has to implement a certain power allocation policy. An example of application of such a model is the case where the performance of terminals operating in unlicensed bands would be enhanced by being allowed to exploit an additional frequency band in which a relay is available. In this network model, each user is selfish and wants to maximize its Shannon transmission rate. We analyze two cases. In the first case, the relaying node is assumed to implement an amplify-and-forward (AF) protocol while in the second case it implements the decode-and-forward (DF) protocol introduced by Cover and El Gamal. For both cases we analyze the existence and uniqueness issues of the equilibrium of

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the aforementioned power allocation games. Several interesting and new results are provided. In particular: 1. The existence of a Nash equilibrium is shown to be always guaranteed in the case of the AF protocol; 2. The performance of a user or the network does not necessarily increase with the transmit power available at the relay; 3. We show that there is naturally a game in interference relay channels (even if the power allocation policy is fixed) when the DF protocol is used; this game is induced by the decentralized choice of the cooperation degree between each source node and the relay node. 3B3.4 Jamming in Wireless Networks: The Case of Several Jammers, Eitan Altman, Konstantin Avrachenkov, Andrey Garnaev

The problem of jamming plays a very important role in ensuring the quality and security of wireless communications, especially now when wireless networks are quickly becoming ubiquitous. Since jamming phenomenon can be considered as a game where a player (jammer) is playing against a user (transmitter), game theory is an appropriate tool for dealing with the jamming problem. In this paper we study how increasing number of jammers impacts the game. Namely, we consider plots with one and two jammers and as an objective function to the user we consider SINR. We show that in all the scenarii the jammers equalize the quality of the best subcarriers for transmitter on as low level as their power constraint allows, meanwhile the user distributes his power among these jamming sub- carriers and in two jammer case the jammers employ time sharing strategies to bring the maximal harm. 3C1 P2P and Social Networks 14:00-15:30 Chair: George Kesidis

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3C1.1 Social Motives in Network Formation: An Experiment, Dennie Van Dolder, Vincent Buskens

Literature on network formation typically assumes that people create and remove relations as to maximize their outcome in the network. It is mostly neglected that people might also care about the outcomes of others when creating and removing links. In the current paper, we develop an experiment to investigate whether people show preferences that involve the outcomes of others during network formation. We find varying evidence for effects of social motives in the settings we compare in the experiment. In the final part of the paper, we discuss some explanations for these findings. 3C1.2 A Simple Reputation Model for BitTorrent-like Incentives, Athichart Tangpong, George Kesidis

We study how BitTorrent exhibits peer clustering in terms of transaction success rate which is based on allocated uplink bandwidths for the purposes

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of file-swapping. The effects of optimistic unchoking and dissemination of choke lists are also considered. Under dynamic uplink assignment, similar grouping results based on differences in how users derive utility from transaction success rates. The “limited information” game requires users periodically assess the effect of a change in uplink. Finally, we conclude with a discussion of how to extend the model to consider the complicating factors such as transient swarm behavior and peer churn. 3C1.3 Strategic Reasoning About Bundling in Swarming Systems, Daniel Menasche, Giovanni Neglia, Don Towsley, Shlomo Zilberstein

The objects of study of this paper are swarming systems, a special kind of peer-to-peer systems where users interested in the same content at the same time cooperate with each other. In particular, we consider the problem of how to combine files into bundles in such systems. First, we analyze the case of a monopoly where a single publisher decides how to aggregate its files so as to satisfy user demands while mitigating its serving costs. We establish conditions for the existence and uniqueness of an equilibrium and how the publisher’s bundling strategy affects its profit. Then, we consider the competitive case where bundling decisions of one publisher affect the outcome of other publishers. Using normal form games we analyze the impact of different system parameters on the Nash equilibrium. 3C1.4 Spread of (Mis)information in Social Networks, Daron Acemoğlu, Asu Özdağlar, Ali ParandehGheibi

This paper discusses how misinformation can affect beliefs among a group of agents and how it interacts with information aggregation. We first show that in social networks where agents involve in Bayesian updating, a finite number of individuals, even if they attempt to spread incorrect information, will have no effect on asymptotic beliefs under relatively mild conditions. This motivates a study of spread of misinformation in social networks where agents use reasonable rule of thumb learning rules. The bulk of the talk will investigate the impact of “influential agents” on the spread of misinformation as a function of network properties and the connectivity of the influential agents.

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3C2 Wireless Networks IV 16:00-17:30 Chair: Eduard Jorswieck 3C2.1 Competitive Scheduling in Wireless Collision Channels with Correlated Channel State, Utku Ozan Candoğan, Ishai Menache, Asuman Özdağlar, Pablo A. Parrilo

We consider a wireless collision channel, shared by a finite number of mobile users who transmit to a common base station. Each user wishes to optimize its individual network utility that incorporates a natural tradeoff between

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throughput and power. The channel quality of every user is affected by global and time-varying conditions at the base station, which are manifested to all users in the form of a common channel state. Assuming that all users employ stationary, state-dependent transmission strategies, we investigate the properties of the Nash equilibrium of the resulting game between users. While the equilibrium performance can be arbitrarily bad (in terms of aggregate utility), we bound the efficiency loss at the best equilibrium as a function of a technology-related parameter. Under further assumptions, we show that sequential best-response dynamics converge to an equilibrium point in finite time, and discuss how to exploit this property for better network usage. 3C2.2 The Role of the Access Point in Wi-Fi Networks with Selfish Nodes, Ilenia Tinnirello, Laura Giarre', Giovanni Neglia

In Wi-Fi networks, mobile nodes compete for accessing the shared channel by means of a random access protocol called Distributed Coordination Function (DCF), which is long term fair. But recent drivers allow users to configure protocol parameters differently from their standard values in order to break the protocol fairness and obtain a larger share of the available bandwidth at the expense of other users. This motivates a game theoretical analysis of DCF. Previous studies have already modeled access to a shared wireless channel in terms of non-cooperative games among the nodes, but they have mainly considered ad hoc mode operation. In this paper we consider the role of the Access Point (AP) in infrastructure mode operation, for mitigating or discouraging such selfish behaviors. Solving a mechanism design problem, we use the AP as a network coordinator, for encouraging node strategies which maximize a global utility function. We analyze both unidirectional and bidirectional (uplink and downlink) traffic scenarios. It is well known that nodes selfishness jeopardize performance, but we show that simple changes to AP operation can let the system achieve optimal performance in spite of nodes selfishness. Instead for the bidirectional scenario the legacy behaviour of an AP is sufficient to guarantee quasi optimal performance.

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3C2.3 Rate Allocation for Satellite Systems with Correlated Channels Based on a Stackelberg Game, Maria-Angeles Vázquez-Castro, Zhu Han, Are Hjørungnes, Ninoslav Marina

In this paper, we consider the problem of capacity allocation for fixed broadband (Ka band) satellite networks with a large coverage and correlated atmospheric channel conditions both in time and space. The transmitted bit rate adapts to the channel by varying the coding rate and the constellation. The network is operated by a single service provider. The model of interest is the downlink where the provider allocates capacity to users with Quality of Service (QoS) guarantees. We first analyze the optimal single-objective optimum allocation by which users’ utilities are maximized.

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We find a closed form for both the proportionally fair and opportunistic allocations. However, these allocations do not show any clear benefit for a profit-seeking service provider because both the efficiency of the network and the user satisfaction with the service cannot be controlled as it mostly depends on the random nature of the correlation properties of the channel. We then propose a Stackelberg game which provides an equilibrium that allows us to prove that 1) the proportionally fair allocation corresponds to a flat-rate pricing model (as used in today’s satellite systems) and 2) Pareto improving policies can be obtained by using differential pricing. From the simulation results, we show that the bit rate allocation based on the Stackelberg formulation yields a network efficiency which is in between the one achieved by the proportionally fair and the opportunistic allocations (as expected from the Pareto improvement), with the advantage that now the efficiency is under full control of the system designer. We also show that the higher the differential pricing the higher the network efficiency. As a general conclusion, both the efficiency of the network and the satisfaction of the users improve with our proposed scheme compared to current designs and therefore a differentiated pricing should be a design goal for this type of systems. 3C2.4 Game Theoretic Rate Control for Mobile Devices, Dimitrios Tsamis, Tansu Alpcan, Nick Bambos

Modern mobile devices offer increased connectivity to heterogeneous wireless networks such as WiFi and 3G. These networks typically exhibit high variability in their characteristics, which poses extra challenges to applications developed to run over them. To address this issue, we propose a game-theoretic rate control scheme for mobile devices. In this noncooperative game formulation of the system the users are assumed the to be selfish in terms of their resource (bandwidth) requests. The information requirements within the model are then simplified by exploiting the available bandwidth measurements provided by a tool called Zeus we developed for this purpose. The formulation is shown to be a potential game, admitting a unique Nash equilibrium. Furthermore, the resulting distributed gradient update algorithm is shown to converge globally. The validity of the model is verified through numerical analysis run on real data, collected by Zeus from different wireless networks. 1

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3C3 Game Theoretic Network Models IV 16:00-17:30 Chair: Corinne Tuoati 3C3.1 How to Hide Information for Later Use on Networks, Steve Alpern, Robbert Fokkink

In an accumulation game a Hider secretly distributes his given total wealth h>1 among n locations while a Searcher picks r locations and confiscates

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the material placed there. The Hider wins if what is left at the remaining locations is at least 1 otherwise the Searcher wins. Accumulation games were originally introduced to study certain covert activities, but the game also relates to secret sharing and food caching. In this paper we introduce a network structure on the game, restricting the Searcher to pick locations that are near and show how this leads to combinatorial considerations. 3C3.2 Selection of Efficient Pure Strategies in Allocation Games, Pierre Coucheney, Corinne Touati, Bruno Gaujal

In this work we consider allocation games and we investigate the following question: under what conditions does the replicator dynamics select a pure strategy? By definition, an allocation game is a game such that the payoff of a player when she takes an action only depends on the set of players who also take the same action. Such a game can be seen as a set of users who share a set of resources, a choice being an allocation to a resource. A companion game (with modified utilities) is introduced. From the payoffs of an allocation game, we define the repercussion utilities: for each player, her repercussion utility is her payoff minus the decrease in marginal payoff that her presence causes to all other players. The corresponding allocation game with repercussion utilities is the game whose payoffs are the repercussion utilities. A simple characterization of those games is given. In such games, if the players select their strategy according to a stochastic approximation of the replicator dynamics, we show that it converges to a Nash equilibrium of the game that is a locally optimal for the initial game. The proof is based on the construction of a potential function for the game. Furthermore, a spectral study of the dynamics shows that no mixed equilibrium is stable, so that the strategies of all players converge to a set of Nash equilibria. Then, martingale argument prove the convergence of the stochastic approximation to a pure point. A discussion of the global/local optimality of the limit points is also included.

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3C3.3 Congestion Games: Equilibria, Convergence, and Complexity, Berthold Vöcking

Congestion games model the allocation of resources by selfish players. For example, players aim at allocating shortest paths in a network. The cost (delay) of a resource (edge) is assumed to be a function of the congestion, i.e., the number of players allocating the resource. We survey results about the existence and complexity of Nash equilibria in different variants of congestion games. Towards this end, we draw a connection to the complexity of local search and elaborate on the complexity class PLS (Polynomial Local Search).

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3C3.4 Convergence of Population Dynamics in Symmetric Routing Games with a Finite Number of Players, Eitan Altman, Vijay Kamble, Vivek Borkar

Routing games, as introduced in the pioneering work of Orda, Rom and Shimkin (1993), are very closely related to the traffic assignment problems as already studied by Wardrop and to congestion games, as introduced by Rosenthal. But they exhibit more complex behavior: often the equilibrium is not unique, and computation of equilibria is typically harder. They cannot be transformed in general into an equivalent global optimization problem as is the case with congestion games and in the traffic assignment problem which possess a potential under fairly general conditions. In this paper we study convergence of various learning schemes to an equilibrium in the problem of routing games. We are able to considerably extend previous published results [1] that were restricted to routing into two parallel links. We study evolutionary-based learning algorithms and establish their convergence for general topologies. 3C4 Security Games 16:00-17:30 Chair: Sudarshan Dhall 3C4.1 Uncertainty in the Weakest Link Security Game, Jens Grossklags, Benjamin Johnson

Individuals in computer networks not only have to invest to secure their private resources from potential attackers, but have to be aware of the existing interdependencies that exist with other network participants. Indeed, a user’s security is frequently negatively impacted by protection failures of even just one other individual, the weakest link. In this paper, we are interested in the impact of bounded rationality and limited information on user payoffs and strategies in the presence of strong weakest-link externalities. As a first contribution, we address the problem of bounded rationality by proposing a simple but novel modeling approach. We anticipate the vast majority of users to be unsophisticated and to apply approximate decision-rules that fail to accurately appreciate the impact of their decisions on others. Expert agents, on the other hand, fully comprehend to which extent their own and others’ security choices affect the network as a whole, and respond rationally. The second contribution of this paper is to address how the security choices by users are mediated by the information available on the severity of the threats the network faces. We assume that each individual faces a randomly drawn probability of being subject to a direct attack. We study how the decisions of the expert user differ if all draws are common knowledge, compared to a scenario where this information is only privately known. We further propose a metric to quantify the value of information available: the payoff difference between complete and incomplete information conditions, divided by the payoff

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under the incomplete information condition. We study this ratio metric graphically and isolate parameter regions where being more informed creates a payoff advantage for the expert agent. 3C4.2 Towards Behavioral Control in Multi-Player Network Games, Andrey Lukyanenko, Andrei Gurtov

Congestion in the routers as well as certain types of resource-exhaustion DoS attacks at the servers can be treated by differentiating packet processing according to previous history of its source. Since it is often difficult to correctly classify packets as legitimate or attack traffic, the scheduling algorithm should tolerate imprecise labeling of packets as long as on the average it punishes misbehaving sources. In this paper, we propose a game-theoretic model based on player rating and formulate the problem in terms of optimal control theory. Applying the Pontryagin maximum principle, we derive necessary control functions to encourage good behavior of network players. As an application of results, we suggest two algorithms for differentiating packet treatment in congested servers and routers. 3C4.3 On the Number and the Distribution of the Nash Equilibria in SuperModular Games and their Impact on the Tipping Set, Sudarshan Dhall, S. Lakshmivarahan, Pramode Verma

In this paper we analyze a class of n-person supermodular games that arise in the context of interdependent security analysis. More specifically, we quantify the number and the distribution of Nash equilibria in pure strategies and their impact on the tipping set. 3C4.4 Stochastic Games for Security in Networks with Interdependent Nodes, Kien Nguyen, Tansu Alpcan, Tamer Başar

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This paper studies a stochastic game theoretic approach to security and intrusion detection in communication and computer networks. Specifically, an Attacker and a Defender take part in a two-player game over a network of nodes whose security assets and vulnerabilities are correlated. Such a network can be modeled using weighted directed graphs with the edges representing the influence among the nodes. The game can be formulated as a non-cooperative zero-sum or nonzero-sum stochastic game. However, due to correlation among the nodes, if some nodes are compromised, the effective security assets and vulnerabilities of the remaining ones will not stay the same in general, which leads to complex system dynamics. We examine existence, uniqueness, and structure of the solution and also provide numerical examples to illustrate our model.

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