Game Theory in Communication Systems

Budhaditya PyneBEE-IV

Roll No: 000910801081Jadavpur University

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What is Game Theory? A Brief History of Game Theory Game Theory Basics with a suitable example An Interesting Analogy with Communication

Systems Non-Cooperative Game Theory in Wireless

Communications Research Coalitional Game Theory in Wireless Networks

Research Game Theory in Routing and Congestion

Control Game Theory in Network Security Scope of Further Research

Topics

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What is Game Theory?

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“…Game Theory is designed to address situations in which the outcome of a person’s decision depends not just on how they choose among several options, but also on the choices made by the people they are interacting with…”

“… Game theory is the study of the ways in which strategic interactions among economic (rational) agents produce outcomes with respect to the preferences (or utilities) of those agents ….”

Game Theory

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Game Theory: A Little History

• Cournot (1838), Bertrand (1883): Economics• J. von Neumann, O. Morgenstern (1944)

• “Theory of Games and Economic Behavior” • Existence of mixed strategy in 2-player game

• J. Nash (1950): Nash Equilibrium • (Nobel Prize in Economic Sciences 1994)

• Selten (1965): Subgame Perfect Equilibrium• Harsani (1967-68): Bayesian (Incomplete Information) Games

• The 80’s• Nuclear disarmament negotiations• Game Theory for Security (Burke)

• More recently:• Auction modeling, mechanism design• Routing, Congestion Control, Channel Access• Network Economics• Network Security• Biology

von Neumann 1903-1957

John F. Nash (1928)

O. Morgenstern 1902-1977

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GAME = (P,A,U)

◦Players (P1; … ; PN): Finite number (N≥2) of decision makers.

◦Action sets (A1; … ;AN): player Pi has a nonempty set Ai of actions.

◦Payoff functions ui : A1x … xAN: R; i = 1;….;N

- materialize players’ preference, - take a possible action profile and assign to it a real number (von Neumann-Morgenstern).

Game Theory Basics

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Cooperative and Non-Cooperative Symmetric and Asymmetric Zero-Sum and Non-Zero Sum Simultaneous and Sequential Static and Dynamic

Types of Games

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A well-known example: The Prisoner’s Dilemma

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What should Prisoner A do to minimize his maximum punishment when:

1. Prisoner B confesses? 2. Prisoner B stays quiet? What should Prisoner B do to minimize his

maximum punishment when:1. Prisoner A confesses? 2. Prisoner A stays quiet?

Strategizing!!: The Min-Max Algorithm

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The Prisoner’s Dilema Contd..

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Routing, Congestion Control and Channel Access

Network Security

Application of Game Theory in Communication Systems

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How do we apply an abstract Mathematical Tool like Game Theory in something as realistic like Communication Systems?

An Inevitable Question!!!

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 Communication Networks consists of several nodes which have to take decisions regarding several aspects like packet switching, packet forwarding, etc.

These nodes are considered as the players. Utility functions are often chosen to correspond to achieved connection rate or similar technical metrics.

An Interesting Analogy

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Non-Cooperative Game Theory in Wireless Networks Research

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Various studies have analyzed radio resource management problems in 802.11 WLAN networks.

In such random access studies, researchers have considered selfish nodes, who try to maximize their own utility (throughput) only, and control their channel access probabilities to maximize their utilities.

Medium Access Games for 802.11 WLAN

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Power control refers to the process through which mobiles in CDMA cellular settings adjust their transmission powers so that they do not create unnecessary interference to other mobiles, trying, nevertheless, to achieve the required Quality of Service.

Power Control may be:1. Centralized2. Distributed

Power Control Games in CDMA systems

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 In such distributed settings, the mobiles can be considered to be selfish agents (players) who try to maximize their utilities (often modeled as corresponding throughputs).

Game theory is considered to be a powerful tool to study such scenarios.

Power Control Games in CDMA systems

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Coalitional game theory is a branch of game theory that deals with cooperative behavior.

 By cooperating, the players can strengthen their position in a given game as well as improve their utilities.

 Coalitional game theory proves to be a powerful tool for modeling cooperative behavior in many wireless networking applications such as cognitive radio networks, wireless system, physical layer security, virtual MIMO.

Cooperative/Coalitional Game Theory in Wireless Networks Research

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It’s a non-cooperative game where the goal of each user is to maximize it’s own bandwidth by selecting its path.

First, the existence of the Nash Equilibrium(NE) is determined because at NE  no user has the incentive to change its routing strategy.

Routing in Max-Min Fair Networks: A Game Theoretic Approach

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 It is investigated how the selfish behavior of the users may affect the performance of the network as a whole.

A concept of observed available bandwidth is introduced on each link which allows a user to find a path with maximum bandwidth under max-min fair congestion control.

 A game-based algorithm is formulated to compute the Nash Equilibrium (NE).

It is seen that by following the natural game course the network converges to an NE.

Routing in Max-Min Fair Networks: A Game Theoretic ApproachContd…

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Routing games◦ users determine

network routes◦ multi-path routing

and traffic splitting is possible

◦ users’ data rates are given and must be routed

Routing Games vs Congestion Control Games

Congestion games users determine their

data rate network routes are

given (single path)

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Game Theory in Network Security

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Who is attacking our communication Systems?

Hackers Terrorists, Criminal Groups

Hacktivists

Disgruntled InsidersForeign Governments

?Game Theory in Communication

Systems 23

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Example: Remote AttackSecurity

Why Game Theory for Security?

Traditional Security Solutions

Attack Defense

Game Theory also helps:

Trust

Incentives

Externalities

Machine Intelligence

Attacker strategy 1 strategy 2 …..

Defender: strategy 1 strategy 2 …..

A mathematical problem! Solution tool: Game

Theory Predict players’ strategies, Build defense mechanisms, Compute cost of security, Understand attacker’s behavior, etc…

E.g.: Rate of Port Scanning IDS Tuning

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Example: Forwarder’s dilemma

Key Concepts

Forwarding has an energy cost of c (c<< 1)Successfully delivered packet: reward of 1

If Green drops and Blue forwards: (1,-c)If Green forwards and Blue drops: (-c,1)

If both forward: (1-c,1-c) If both drop: (0,0)

Each player is trying to selfishly maximize it’s net gain.

What can we predict?Game Theory in Communication

Systems 25

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Example: Forwarder’s dilemma

Key Concepts

Game:Players: Green, BlueActions: Forward (F), Drop (D)Payoffs: (1-c,1-c), (0,0), (-c,1), (1,-c)

Matrix representation: Actions of Green

Actions of Blue

Reward of BlueReward of Green

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Nash equilibrium:“…a solution concept of a game involving two

or more players, in which no player has anything to gain by changing his own strategy unilaterally…”

Equilibrium Concept

John F. Nash (1928)

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3 Communication Security Game Models

Intruder Game

p

1-p

AliceTrudy

BobX Y Z

AvailabilityAttack

IntelligentVirus

aNormal traffic

Virus b

Xn

Detection

If Xn > l => Alarm

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M’ ¹ M

Intruder (Trudy)

What if it ispossible that:

M

Intruder Game

Scenario:

Network

Source (Alice)

User (Bob)

M

Encryption is not always practical ….Formulation: Game between Intruder and User

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Intruder Game: Binary

Y

• Payoffs:

• Strategies (mixed i.e. randomized)• Trudy: (p0,p1), Bob: (q0,q1)

Alice

TrudyBob

Intercept

• One shot, simultaneous choice game

• Nash Equilibrium?

Z

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What if the receiver (Bob) can verify the message?(by paying a cost and using a side secure channel)

p

1-p

AliceTrudy

BobX Y Z

Pay: V

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Intelligent Virus GameScenario

aNormal traffic

Virus b

Xn

Detection

If Xn > l => Alarm, ….Assume a known

Detection system: choose l to minimize cost of infection + clean up

Virus: choose b to maximize infection cost

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Intelligent Virus Game (IDS)

Smart virus designer picks very large b, so that the cost is always high ….Regardless of !l

0 10 20 30 40 50 60 70 80 90 1001

1.2

1.4

1.6

1.8

2

2.2

2.4

(/sec)

Virus G

ain

: Lin

ear

0=5

0=10

0=15

b

Scenario

aNormal traffic

Virus b

Xn

Detection

If Xn > l => Alarm, ….

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Intelligent Virus Game (IPS) Modified Scenario

aNormal traffic

Virus b

XnDetection

If Xn > l => Alarm

• Detector: buffer traffic and test threshold• Xn < l process• If Xn > l Flush & Alarm

• Game between Virus (b) and Detector (l)

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Availability Attack Models!

Tree-Link Game:

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Consider a tree with € links and n nodes. Let Ƭ be the set of spanning trees.

To get all the nodes connected in a cycle-free way, the Network Manager/Defender chooses a spanning tree TϵƬ of the network

The attacker simultaneously chooses a link eϵ€ to attack

The attacker wins if the attacked link belongs to the chosen spanning tree; the Defender wins elsewise

Tree-Link Game

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Game( modeled as a one-shot 2 player game)◦ Graph = (nodes V, links E, spanning trees T)

Defender: chooses T T

Attacker: chooses e E (+ “No Attack”)

◦ Rewards Defender: -1eT Attacker: 1eT - µe (µe cost of attacking e)

Model

Example:

Defender: 0Attacker: - µ2

Defender: -1Attacker: 1- µ1

– Defender : choose a distribution on T, to minimize the expected attack loss

--Attacker: Choose a distribution on E, to maximize the attack gain

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Let’s Play a Game!

Graph Most vulnerable links

Chance 1/2

Chance 4/7>1/2

a)

b)

c)

Assume: zero attack cost µe=0

1/2

1/2

1/7

1/7

1/7

1/7

1/71/7

1/7

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Critical Subset of Links

• Definition 1&2: For any nonempty subset E Ε

1. M(E) = min{| TE|, TТ} (minimum number of links E has in common with any spanning tree)

2. Vulnerability of E (E) = M(E)/|E| (minimum fraction of links E has in common with any spanning tree)

• Definition 3: A nonempty subset C Ε is said to be critical if (C) = maxE Ε((E))

(C has maximum vulnerability) vulnerability of graph ((G)) := vulnerability of critical subset

123 4

567

E={1,4,5}|T E|=2M(E) =1

Defender: choose trees that minimally cross critical subset

(E) = 1/3

(G)=1 (G)=1/2 (G)=4/7

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Critical Subset Attack Theorem

Theorem 1:There exists a Nash Equilibrium where

• Attacker attacks only the links of a critical set C, with equal probabilities

• Defender chooses only spanning trees that have a minimal intersection with C, and have equal likelihood of using each link of C, no larger than that of using any link not in C. [Such a choice is possible.]

There exists a polynomial algorithm to find C [Cunningham 1982]

Theorem generalizes to a large class of games.Game Theory in Communication

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Some implications

If ν ≤ 0: Attacker: “No Attack”Defender can invest to make µ highDeter attacker from attacking• Need to randomize choice of tree

Edge-Connectivity is not always the right metric!

ν= 3/4 ν= 2/3 ν= 3/5

2/3 > 3/5

Network in b) is more vulnerable than network in c)Additional link

Network Design

a) b) c)

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Availability Games◦ Critical set

Vulnerability ((G)): a metric more refined than edge-connectivity

Analyzing NE helps determine most vulnerable subset of links Importance in topology design Polynomial-time algorithm to compute critical set

◦ Generalization Set of resources for mission critical task

Most vulnerable subset of resources.

Conclusion

Intruder and Intelligent Virus Games:• Most aggressive attackers are not the most dangerous ones• Mechanisms to deter attackers from attacking

Game Theory helps for a better understanding

of the Security problem!

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A certain number of issues◦ Costs model

Not based on solid ground

◦ Mixed strategy equilibrium How to interpret it?

◦ Nash equilibrium computation In general difficult to compute

This is an “young” research field!

Game Theory for Airport SecurityARMOR (LAX)

Airports create security systems and terrorists seek out breaches.

Placing checkpoint Allocate canine units

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• Repeated versions of the games– More realistic models– Applications: Attack Graphs

• Collaborative Security– Team of Attackers vs Team of Defenders– Trust and Security– Role of Information

• Security of Cloud Computing– Are you willing to give away your information?

• Policing the Internet– Who is responsible for security flaws?

Further Scope of Research

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Thank you!Questions?

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