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Interdomain Routing and Games
Michael Schapira
Joint work with Hagay Levin
and Aviv Zohar
האוניברסיטה העברית בירושליםהאוניברסיטה העברית בירושליםThe Hebrew University of JerusalemThe Hebrew University of Jerusalem
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The Agenda
• An introduction to interdomain routing (a networking approach).
• A Distributed Algorithmic Mechanism Design (DAMD) perspective (an economic approach).
• Our Results:– A formulation of interdomain routing as a game.– Realistic settings in which BGP is immune to rational
manipulations.– …
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An Introduction to An Introduction to Interdomain RoutingInterdomain Routing
(A Networking Approach)(A Networking Approach)
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Interdomain Routing
Establish routes between Autonomous Systems (ASes).
Currently done only by the Border Gateway Protocol (BGP).
AT&T
Qwest
Comcast
UUNET
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Why is Interdomain Routing Hard?
• Route choices are based on local policies.
• Expressiveness: Policies are complex.
• Autonomy: Policies are uncoordinated
AT&T
Qwest
Comcast
UUNET
My link to UUNET is forbackup purposes only.
Load-balance myoutgoing traffic.
Always chooseshortest paths.
Avoid routes through AT&T ifat all possible.
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Interdomain Routing
• Routes to every destination AS are computed independently.
• There is an AS graph G=<N,L>. – N consists of n source nodes 1,…,n and
a destination node d.
– L represents physical links between ASes.
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Interdomain Routing
receive routes from neighbours
choose“best”
neighbour
send updatesto neighbours
• Every source-node i is defined by a valuation function vi that assigns a non-negative value to each (simple) route from i to d.
• The computation performed by a single node is an infinite sequence of stages:
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Interdomain Routing
• The route assignment reached by BGP forms a confluent routing tree rooted in d.– Routes are consistent (route choices depend
on neighbours’ choices).– Routes are loop-free (nodes announce full
routes).
• The final route assignment is stable.– Every node prefers its assigned route over
any other available route.
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Example of Stability
1 2
d
Prefer routes
through 2
Prefer routes through 1
2, I’m available
1, my routeis 2d
1, I’m available
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Assumptions on the Network
• The network is asynchronous.– Nodes can be activated in different timings.
– Update messages can be arbitrarily delayed along selective links.
• Network malfunctions are possible.– Link and node failures.
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BGPPros:
• Nodes need have no a-priori knowledge about the network topology or about other nodes.
• The protocol is adaptive to changes in network topology (link and node failures).
• ….
Cons:
• The lack of global coordination might result in persistent route oscillations (protocol divergence).
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Example of Instability: Oscillation
1 2
d
BGP might oscillateforever between
1d, 2dand
12d, 21d
Prefer routes
through 2
Prefer routes through 1
1, 2, I’m thedestination
1, my routeis 2d
2, my routeis 1d
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The Hardness of Stability
• Theorem: Determining whether a ``stable solution’’ exists is NP-Hard. [Griffin-Wilfong]
• Theorem: Determining whether a ``stable solution’’ exists requires exponential communication between the source-nodes.– Independent of the P-NP assumption.– Communication complexity is linear in the “size” of the local preferences
of nodes.
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• Networking researchers seek constraints that guarantee BGP stability (for any timing, even in the presence of network malfunctions). [Balakrishnan, Feamster, Gao, Griffin, Jaggard, Johari, Ramachandran, Rexford, Shepherd, Sobrinho, Wilfong, …]
• A realistic and well known set of such constraints are the Gao-Rexford constraints.– The Internet is formed by economic forces.– ASes sign long-term contracts that determine who
provides connectivity to whom.
Guaranteeing Robust Convergence
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Gao-Rexford FrameworkNeighboring pairs of ASes have one of:
– a customer-provider relationship(One node is purchasing connectivity fromthe other node.)
– a peering relationship(Nodes have offered to carry each other’stransit traffic, often to shortcut a longer route.)
peerproviders
customers
peer
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Dispute Wheels
• If BGP oscillates, the valuation functions and the topology of the network induce a structure called a Dispute Wheel. [Griffin-Shepherd-Wilfong]
• The absence of a Dispute Wheel ensures robust BGP convergence.
• The Gao-Rexford constraints are a special case of “No Dispute Wheel”. [Gao-Griffin-Rexford]
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Dispute Wheels
• A Dispute Wheel: – A sequence of nodes ui and routes Ri, Qi.
– ui prefers RiQi+1 over Qi.
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Example of a Dispute Wheel
1 2
d
Prefer routes
through 2
Prefer routes through 1
2
1
d
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A DAMD PerspectiveA DAMD Perspective
(An Economic Approach)(An Economic Approach)
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Do Nodes Always Adhere to the Protocol?
• BGP was designed to guarantee connectivity between trusted and obedient parties.
• The commercial Internet: ASes are owned by economic and often competing entities.– Might deviate from BGP if it suits their interests.
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Two Research Agendas
• Security research – Malicious nodes.
– Cyptographic modifications of BGP (S-BGP)
• Distributed Algorithmic Mechanism Design [Feigenbaum-Papadimitriou-Shenker]
– Rational nodes.– Seeks realistic conditions for which BGP is
incentive-compatible. [Feigenbaum-Papadimitriou-Sami-Shenker]
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Our ResultsOur Results
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Our Main Results• A novel game-theoretic model of interdomain
routing.
• A surprising connection between the two research agendas (security and DAMD).
• Theorem: (bad news): BGP is not incentive-compatible even if No Dispute Wheel holds.
• Theorem: (good news): Cryptographic modifications of BGP (e.g., S-BGP) are incentive-compatible if No Dispute Wheel holds (no monetary transfers).
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Interdomain RoutingInterdomain RoutingGamesGames
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A Static Game
• The source-nodes are the strategic agents (their valuation functions define their types).
• Each source-node chooses an outgoing edge.– Choices are simultaneous.
• A node’s payoff is:– vi(R) if the route R from i to d is induced by the
nodes’ choices.– 0 otherwise.
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A Static Game
• A pure Nash equilibrium is a set of nodes’ choices from which no node wishes to unilaterally deviate.
• Pure Nash equilibria = stable routing outcomes
1 2
d
Prefer routes
through 2
Prefer routes
through 1
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The Convergence Game
• The game consists of an infinite number of rounds.
• A node that is activated in a certain round can perform the following actions:– Read update messages announcing routes.
– Send update messages announcing routes.
– Choose a neighbouring node to forward traffic to.
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The Convergence Game
• There exists an adversarial entity called the scheduler that is in charge of: – Deciding which nodes are activated in each round.– Delaying update messages along selective links.– Removing links and nodes from the AS graph.
• Informally, a node’s strategy is its choice of a routing protocol.– Executing BGP is a strategy.
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The Convergence Game
• A route is said to be stable if from some round onwards every node on the route forwards traffic to the next-hop node on that route.
• The payoff of node i from the game is:– vi(R) if there is a route R from i to d which is
stable.
– 0 otherwise.
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BGP and Incentives
• A node is said to deviate from BGP (or to manipulate BGP) if it does not follow BGP.
• What forms of manipulation are available to nodes?– Misreporting preferences.– Reporting inconsistent information.– Announcing nonexistent routes. – Denying routes.– …
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BGP and Incentives
Two possible incentive-related requirements from BGP:
• Incentive-compatibility: No unilateral deviation from BGP by an AS can strictly improve the routing outcome of that AS.
• Collusion-proofness: No deviation from BGP by coalitions of ASes of any size can strictly improve the routing outcome of even a single AS in the coalition without strictly harming another [Feigenbaum-S-
Shenker].
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About the Convergence Game
• The game is complex.– Multi-round.– Asynchronous.– Partial-information
• No monetary transfers!– Very rare in mechanism design.– Unlike most works on incentive-compatibility and
interdomain routing– More realistic.
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Known Results
. . .
. . . .
d
k i
IFvk(R1) > vk(R2)
R2
R1
THENvi((i,k)R1) > vi((i,k)R2)
Valuations are policy consistentiff, for all routes R1 and R2
(analogous toisotonicity [Sob.03])
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Known results
• Policy consistency is known to hold for interesting special cases:– Shortest-path routing.– Next-hop policies.
• Theorem: If No Dispute Wheel and Policy Consistency hold, then BGP is incentive-compatible, and even collusion-proof. [Feigenbaum-Ramachandran-S, Feigenbaum-S-Shenker]
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Known results
• A Problem: Policy Consistency is unrealistic.– Too strong.
• Can it be removed?
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Realistic Settings in which Realistic Settings in which BGP is Incentive-Compatible BGP is Incentive-Compatible
and Collusion-Proofand Collusion-Proof
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Is BGP Incentive-Compatible?
• Theorem: BGP is not incentive compatible even in Gao-Rexford settings.
m 1
2
d
m1dm12d
2md2d
12d1d
with manipulation
m 1
2
d
m1dm12d
2md2d
12d1d
without manipulation
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• We define the following property:
–Route verification means that an AS can verify that a route announced by a neighbouring AS is available.
• Route verification can be achieved via security tools (S-BGP etc.).–Not an assumption on the nodes!
Can we fix this?
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• Many forms of manipulation are still available:– Misreporting preferences over available
routes.– Reporting inconsistent information.– Denying routes.– …
Does this solve the problem?
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• Theorem: If the “No Dispute Wheel” condition holds, then BGP with route verification is incentive-compatible.
• Theorem: If the “No Dispute Wheel” condition holds, then BGP with strong route verification is collusion-proof.
Our Main Results
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Dispute Wheels – A Reminder
• A Dispute Wheel: – A sequence of nodes ui and routes Ri, Qi.
– ui prefers RiQi+1 over Qi.
The Gao-Rexford constraintsare a special case of
the “No Dispute Wheel”condition.
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• Theorem: If the “No Dispute Wheel” condition holds, then BGP with route verification is incentive-compatible.
• Proof (sketch): – By contradiction. – Assume that the “No Dispute Wheel”
condition holds, and that BGP is not incentive-compatible.
– We present sequences of nodes and routes that form a dispute wheel.
BGP with Route Verification
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Proof Sketch
d
s
Ts
Ms
• Let s be the manipulator.
• Let T be the routing tree reached if all nodes follow the protocol.
• Let M be the the routing tree reached after s rationally manipulates BGP.
• vs(Ms) > vs(Ts)
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Proof Sketch
d
s
1Ts
Ms
M1
T1
• There must exist a node i on Ms such that Mi≠Ti
• Let 1 be the node closest to d on Ms with this property.
• For each node i that is closer to d on Ms it holds that Mi=Ti.
• This implies: v1(T1) > v1(M1)
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Proof Sketch
d
s
1
2
Ts
Ms
M1
T1
T2
M2
• Similarly, Let 2 be the node i closest to d on T1 such that Mi≠Ti.
• This implies: v2(M2) > v2(T2)
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Proof Sketch
d
s
1
2
3
4
Ts
Ms
M1
T1
T2
M2
M3
T3
T4
k
Mk
Tk
• We choose 3,4,5,… in asimilar manner.
• Eventually some nodewill appear twice (assume that this nodeis s).
• We have a dispute wheel!
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• Why do we need route verification?
• The manipulator can lie about its route.
• For instance, k might believe that s’s route in M is Ls.
• Still,
vs(Ms) > vs(Ts) > vs(Ls)
d
s
1
2
3
4
k Ts
Ms
M1
T1
T2
M2
M3
T3
T4
Tk
Mk
Ls
Proof Sketch
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• Theorem: If the “No Dispute Wheel” condition holds, then BGP with route verification is collusion-proof.
• A Problem: Is route verification achievable even in the presence many manipulators?
BGP with Route Verification
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• Corollary: If No Dispute Wheel holds, then BGP is Pareto optimal.
• Pareto optimality means that BGP’s outcome is such that there is no other outcome that is:– Strictly preferred by one node.
– Weakly preferred by all other nodes.
BGP is Socially Just
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• The total social welfare of a routing outcome is the sum of values nodes assign to their routes = ∑i vi(Pi).
• No Dispute Wheel and Policy Consistency guarantee BGP convergence to a social-welfare maximizing solution. [Feigenbaum-Ramachandran-S]
What About Social-Welfare?
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Approximating Social Welfare
• Theorem: Obtaining an approximation to the optimal social welfare is impossible unless P=NP, even in Gao-Rexford settings.(Improvement on a bound achieved by [Feigenbaum,Sami,Shenker])
• Theorem: Exponential communication is required in order to achieve an approximation of to the social welfare.
2/1nO
1nO
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Conclusions
• The main results:– Bad news: BGP is not incentive-compatible
even if No Dispute Wheel holds.
– Good news: A modification of BGP (route verification) is incentive-compatible.
• Helps explain BGP’s relative resilience to manipulations in practice.
![Page 53: Interdomain Routing and Games Michael Schapira Joint work with Hagay Levin and Aviv Zohar האוניברסיטה העברית בירושלים The Hebrew University of Jerusalem](https://reader033.vdocuments.site/reader033/viewer/2022051622/56649d4d5503460f94a2ca18/html5/thumbnails/53.jpg)
Conclusions
• Our results should motivate research on guaranteeing route verification in the Internet.
• Where’s the justice?– Bad news: Social-welfare optimization
might be hopeless.
– Good news: BGP is Pareto optimal.
![Page 54: Interdomain Routing and Games Michael Schapira Joint work with Hagay Levin and Aviv Zohar האוניברסיטה העברית בירושלים The Hebrew University of Jerusalem](https://reader033.vdocuments.site/reader033/viewer/2022051622/56649d4d5503460f94a2ca18/html5/thumbnails/54.jpg)
Follow Up Works
• “Best-reply mechanisms” (with Noam Nisan and Aviv Zohar)– Extensions to more general game-theoretic
settings.
• Work in progress (with Rahul Sami and Aviv Zohar)– More on BGP convergence and selfishness.
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• Characterizing robust BGP convergence (“No dispute wheel” is sufficient but not necessary).
• Does robust BGP convergence with route verification imply incentive compatibility?
• Can network formation games help explain the Internet’s commercial structure?
Open Questions
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• Generalize the model to allow other forms of “attacks” [Butler-Farley-McDaniel-Rexford]
Open Questions
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Thank YouThank You