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34
Interdomain routing and games
 In STOC ’08
"... We present a gametheoretic model that captures many of the intricacies of interdomain routing in today’s Internet. In this model, the strategic agents are source nodes located on a network, who aim to send traffic to a unique destination node. The interaction between the agents is dynamic and compl ..."
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Cited by 39 (15 self)
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We present a gametheoretic model that captures many of the intricacies of interdomain routing in today’s Internet. In this model, the strategic agents are source nodes located on a network, who aim to send traffic to a unique destination node. The interaction between the agents is dynamic and complex – asynchronous, sequential, and based on partial information. Bestreply dynamics in this model capture crucial aspects of the only interdomain routing protocol de facto, namely the Border Gateway Protocol (BGP). We study complexity and incentiverelated issues in this model. Our main results are showing that in realistic and wellstudied settings, BGP is incentivecompatible. I.e., not only does myopic behaviour of all players converge to a “stable ” routing outcome, but no player has motivation to unilaterally deviate from the protocol. Moreover, we show that even coalitions of players of any size cannot improve their routing outcomes by collaborating. Unlike the vast majority of works in mechanism design, our results do not require any monetary transfers (to or by the agents).
Designing networks with good equilibria
 In SODA ’08
, 2007
"... In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network co ..."
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Cited by 34 (4 self)
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In a network with selfish users, designing and deploying a protocol determines the rules of the game by which end users interact with each other and with the network. We study the problem of designing a protocol to optimize the equilibrium behavior of the induced network game. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge costsharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, singlesink and multicommodity networks, different classes of costsharing methods, and different measures of the inefficiency of equilibria. One of our main technical tools is a complete characterization of the uniform costsharing protocols—protocols that are designed without foreknowledge of or assumptions on the network in which they will be deployed. We use this characterization result to identify the optimal uniform protocol in several scenarios: for example, the Shapley protocol is optimal in directed graphs, while the optimal protocol in undirected graphs, a simple priority scheme, has exponentially smaller worstcase price of anarchy than the Shapley protocol. We also provide several matching upper and lower bounds on the bestpossible performance of nonuniform costsharing protocols.
Searching for stability in interdomain routing
 in Proc. of INFOCOM, 2009
"... Abstract—The Border Gateway Protocol (BGP) handles the task of establishing routes between the Autonomous Systems (ASes) that make up the Internet. It is known that it is possible for a group of ASes to define local BGP policies that lead to global BGP protocol oscillations. We close a long standing ..."
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Cited by 21 (4 self)
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Abstract—The Border Gateway Protocol (BGP) handles the task of establishing routes between the Autonomous Systems (ASes) that make up the Internet. It is known that it is possible for a group of ASes to define local BGP policies that lead to global BGP protocol oscillations. We close a long standing open question by showing that, for any network, if two stable routing outcomes exist then persistent BGP route oscillations are possible. This is the first nontrivial necessary condition for BGP safety. It shows that BGP safety must always come at the price of severe restrictions on ASes ’ expressiveness in their choice of routing policies. The technical tools used in our proof may be helpful in the detection of potential route oscillations and their debugging. We also address the question of how long it takes BGP to converge to a stable routing outcome. We analyze a formal measure of the convergence time of BGP for the policy class defined by Gao and Rexford, which is said to accurately depict the business structure underlying the Internet. We prove that, even for this restricted class of preferences, the convergence time might be linear in the size of the network. However, we show a much more reasonable bound if the network structure is similar to the current Internet: we prove that the number of phases required for convergence is bounded by approximately twice the depth of the customerprovider hierarchy. I.
Designing Network Protocols for Good Equilibria
, 2009
"... Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network costsharing games, where the set ..."
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Cited by 13 (1 self)
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Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network costsharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge costsharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal costsharing protocols for undirected and directed graphs, singlesink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the costsharing protocols that only induce network games with purestrategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs, and that simple priority protocols are essentially optimal in undirected graphs.
Distributed computing with adaptive heuristics
 In Proceedings of Innovations in Computer Science ICS
, 2011
"... Abstract: We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics [16], i.e., simple and unsophisticated rules of behavior, e.g., repeatedly “best replying ” to others ’ actions, and minimizing “regret”, that ..."
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Cited by 12 (4 self)
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Abstract: We use ideas from distributed computing to study dynamic environments in which computational nodes, or decision makers, follow adaptive heuristics [16], i.e., simple and unsophisticated rules of behavior, e.g., repeatedly “best replying ” to others ’ actions, and minimizing “regret”, that have been extensively studied in game theory and economics. We explore when convergence of such simple dynamics to an equilibrium is guaranteed in asynchronous computational environments, where nodes can act at any time. Our research agenda, distributed computing with adaptive heuristics, lies on the borderline of computer science (including distributed computing and learning) and game theory (including game dynamics and adaptive heuristics). We exhibit a general nontermination result for a broad class of heuristics with bounded recall—that is, simple rules of behavior that depend only on recent history of interaction between nodes. We consider implications of our result across a wide variety of interesting and timely applications: game theory, circuit design, social networks, routing and congestion control. We also study the computational and communication complexity of asynchronous dynamics and present some basic observations regarding the effects of asynchrony on noregret dynamics. We believe that our work opens a new avenue for research in both distributed computing and game theory.
The price of stochastic anarchy
 In SAGT ’08: Proceedings of the First Annual International Symposium on Algorithmic Game Theory
, 2008
"... Abstract. We consider the solution concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of (Nash) anarchy for quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages th ..."
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Cited by 11 (5 self)
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Abstract. We consider the solution concept of stochastic stability, and propose the price of stochastic anarchy as an alternative to the price of (Nash) anarchy for quantifying the cost of selfishness and lack of coordination in games. As a solution concept, the Nash equilibrium has disadvantages that the set of stochastically stable states of a game avoid: unlike Nash equilibria, stochastically stable states are the result of natural dynamics of computationally bounded and decentralized agents, and are resilient to small perturbations from ideal play. The price of stochastic anarchy can be viewed as a smoothed analysis of the price of anarchy, distinguishing equilibria that are resilient to noise from those that are not. To illustrate the utility of stochastic stability, we study the load balancing game on unrelated machines. This game has an unboundedly large price of Nash anarchy even when restricted to two players and two machines. We show that in the two player case, the price of stochastic anarchy is 2, and that even in the general case, the price of stochastic anarchy is bounded. We conjecture that the price of stochastic anarchy is O(m), matching the price of strong Nash anarchy without requiring player coordination. We expect that stochastic stability will be useful in understanding the relative stability of Nash equilibria in other games where the worst equilibria seem to be inherently brittle.
On the Equilibria of Alternating Move Games
 In Proceedings of the ACMSIAM Symposium on Discrete Algorithms
, 2010
"... We consider computational aspects of alternating move games, repeated games in which players take actions at alternating time steps rather than playing simultaneously. We show that alternating move games are more tractable than simultaneous move games: we give an FPTAS for computing an ɛapproximate ..."
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Cited by 10 (2 self)
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We consider computational aspects of alternating move games, repeated games in which players take actions at alternating time steps rather than playing simultaneously. We show that alternating move games are more tractable than simultaneous move games: we give an FPTAS for computing an ɛapproximate equilibrium of an alternating move game with any number of players. In contrast, it is known that for k ≥ 3 players, there is no FPTAS for computing Nash equilibria of simultaneous move repeated games unless P = P P AD. We also consider equilibria in memoryless strategies, which are guaranteed to exist in two player games. We show that for the special case of k = 2 players, all but a negligible fraction of games admit an equilibrium in pure memoryless strategies that can be found in polynomial time. Moreover, we give a PTAS to compute an ɛapproximate equilibrium in pure memoryless strategies in any 2 player game that admits an exact equilibrium in pure memoryless strategies. 1
There’s something about MRAI: Timing diversity can exponentially worsen BGP convergence
 IN PROC. OF INFOCOM
, 2011
"... To better support interactive applications, individual network operators are decreasing the timers that affect BGP convergence, leading to greater diversity in the timer settings across the Internet. While decreasing timers is intended to improve routing convergence, we show that, ironically, the r ..."
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Cited by 9 (2 self)
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To better support interactive applications, individual network operators are decreasing the timers that affect BGP convergence, leading to greater diversity in the timer settings across the Internet. While decreasing timers is intended to improve routing convergence, we show that, ironically, the resulting timer heterogeneity can make routing convergence substantially worse. We examine the widelyused Min Route Advertisement Interval (MRAI) timer that ratelimits update messages to reduce router overhead. We show that, while routing systems with homogeneous MRAI timers have linear convergence time, diverse MRAIs can cause exponential increases in both the number of BGP messages and the convergence time (as measured in “activations”). We prove tight upper bounds on these metrics in terms of MRAI timer diversity in general disputewheelfree networks and economically sensible (GaoRexford) settings. We also demonstrate significant impacts on the data plane: blackholes sometimes last throughout the routeconvergence process, and forwarding changes, at best, are only polynomially less frequent than routing changes. We show that these problems vanish in contiguous regions of the Internet with homogeneous MRAIs or with nexthopbased routing policies, suggesting practical strategies for mitigating the problem, especially when all routers are administered by one institution.
Mixing time and stationary expected social welfare of logit dynamics. Theory of Computing Systems
, 2013
"... Abstract We study logit dynamics [Blu93] for strategic games. At every stage of the game a player is selected uniformly at random and she plays according to a noisy bestresponse dynamics where the noise level is tuned by a parameter β. Such a dynamics defines a family of ergodic Markov chains, ind ..."
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Cited by 8 (7 self)
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Abstract We study logit dynamics [Blu93] for strategic games. At every stage of the game a player is selected uniformly at random and she plays according to a noisy bestresponse dynamics where the noise level is tuned by a parameter β. Such a dynamics defines a family of ergodic Markov chains, indexed by β, over the set of strategy profiles. Our aim is twofold: On the one hand, we are interested in the expected social welfare when the strategy profiles are random according to the stationary distribution of the Markov chain, because we believe it gives a meaningful description of the longterm behavior of the system. On the other hand, we want to estimate how long it takes, for a system starting at an arbitrary profile and running the logit dynamics, to get close to the stationary distribution; i.e., the mixing time of the chain. In this paper we study the stationary expected social welfare for the 3player CK game [CK05], for 2player coordination games (the same class of games studied in [Blu93]), 2player anticoordination games, and for a simple nplayer game. For all these games, we give almosttight upper and lower bounds on the mixing time of logit dynamics.