Results 1  10
of
18
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 32 (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.
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 32 (10 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).
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 7 (2 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.
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 7 (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.
BGP Safety with Spurious Updates
"... Abstract—We explore BGP safety, the question of whether a BGP system converges to a stable routing, in light of several BGP implementation features that have not been fully included in the previous theoretical analyses. We show that Route Flap Damping, MRAI timers, and other intrarouter features ca ..."
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Cited by 6 (1 self)
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Abstract—We explore BGP safety, the question of whether a BGP system converges to a stable routing, in light of several BGP implementation features that have not been fully included in the previous theoretical analyses. We show that Route Flap Damping, MRAI timers, and other intrarouter features can cause a router to briefly send “spurious ” announcements of lesspreferred routes. We demonstrate that, even in simple configurations, this shortterm spurious behavior may cause longterm divergence in global routing. We then present DPVP, a general model that unifies these sources of spurious announcements in order to examine their impact on BGP safety. In this new, more robust model of BGP behavior, we derive a necessary and sufficient condition for safety, which furthermore admits an efficient algorithm for checking BGP safety in most practical circumstances — two complementary results that have been elusive in the past decade’s worth of classical studies of BGP convergence in more simple models. We also consider the implications of spurious updates for wellknown results on dispute wheels and safety under filtering. I.
An algorithmic game theory primer
, 2008
"... We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1 ..."
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Cited by 5 (0 self)
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We give a brief and biased survey of the past, present, and future of research on the interface of theoretical computer science and game theory. 1
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 ..."
Abstract

Cited by 5 (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 4 (2 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.
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 3 (1 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