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The Complexity of Pure Nash Equilibria
, 2004
"... We investigate from the computational viewpoint multiplayer games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLScomplete in general. ..."
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Cited by 173 (6 self)
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We investigate from the computational viewpoint multiplayer games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLScomplete in general. We discuss implications to nonatomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.
Iterative Combinatorial Auctions: Achieving Economic and Computational Efficiency
 DEPARTMENT OF COMPUTER AND INFORMATION SCIENCE, UNIVERSITY OF PENNSYLVANIA
, 2001
"... This thesis presents new auctionbased mechanisms to coordinate systems of selfinterested and autonomous agents, and new methods to design such mechanisms and prove their optimality... ..."
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Cited by 160 (21 self)
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This thesis presents new auctionbased mechanisms to coordinate systems of selfinterested and autonomous agents, and new methods to design such mechanisms and prove their optimality...
Approximating GameTheoretic Optimal Strategies for Fullscale Poker
 IN INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2003
"... The computation of the first complete approximations of gametheoretic optimal strategies for fullscale poker is addressed. Several abstraction techniques are combined to represent the game of 2player Texas Hold'em, having size O(10^18), using closely related models each having size ..."
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Cited by 159 (22 self)
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The computation of the first complete approximations of gametheoretic optimal strategies for fullscale poker is addressed. Several abstraction techniques are combined to represent the game of 2player Texas Hold'em, having size O(10^18), using closely related models each having size .
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 144 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Computing the optimal strategy to commit to
 IN PROCEEDINGS OF THE 7TH ACM CONFERENCE ON ELECTRONIC COMMERCE (ACMEC
, 2006
"... In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models a ..."
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Cited by 144 (22 self)
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In multiagent systems, strategic settings are often analyzed under the assumption that the players choose their strategies simultaneously. However, this model is not always realistic. In many settings, one player is able to commit to a strategy before the other player makes a decision. Such models are synonymously referred to as leadership, commitment, or Stackelberg models, and optimal play in such models is often significantly different from optimal play in the model where strategies are selected simultaneously. The recent surge in interest in computing gametheoretic solutions has so far ignored leadership models (with the exception of the interest in mechanism design, where the designer is implicitly in a leadership position). In this paper, we study how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normalform and Bayesian games. We give both positive results (efficient algorithms) and negative results (NPhardness results).
The price of routing unsplittable flow
 In Proc. 37th Symp. Theory of Computing (STOC
, 2005
"... The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to d ..."
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Cited by 137 (3 self)
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The essence of the routing problem in real networks is that the traffic demand from a source to destination must be satisfied by choosing a single path between source and destination. The splittable version of this problem is when demand can be satisfied by many paths, namely a flow from source to destination. The unsplittable, or discrete version of the problem is more realistic yet is more complex from the algorithmic point of view; in some settings optimizing such unsplittable traffic flow is computationally intractable. In this paper, we assume this more realistic unsplittable model, and investigate the ”price of anarchy”, or deterioration of network performance measured in total traffic latency under the selfish user behavior. We show that for linear edge latency functions the price of anarchy is exactly 2.618 for weighted demand and exactly 2.5 for unweighted demand. These results are easily extended to (weighted or unweighted) atomic ”congestion games”, where paths are replaced by general subsets. We also show that for polynomials of degree d edge latency functions the price of anarchy is dΘ(d). Our results hold also for mixed strategies. Previous results of Roughgarden and Tardos showed that for linear edge latency functions the price of anarchy is exactly 4 3 under the assumption that each user controls only a negligible fraction of the overall traffic (this result also holds for the splittable case). Note that under the assumption of negligible traffic pure and mixed strategies are equivalent and also splittable and unsplittable models are equivalent. 1
An introduction to collective intelligence
 Handbook of Agent technology. AAAI
, 1999
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Complexity Results about Nash Equilibria
, 2002
"... Noncooperative game theory provides a normative framework for analyzing strategic interactions. ..."
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Cited by 136 (11 self)
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Noncooperative game theory provides a normative framework for analyzing strategic interactions.
Stability of Multipacket Slotted Aloha with Selfish Users and Perfect Information
, 2003
"... Aloha is perhaps the simplest and moststudied medium access control protocol in existence. Only in the recent past, however, have researchers begun to study the performance of Aloha in the presence of selfish users. In this paper, we present a gametheoretic model of multipacket slotted Aloha with ..."
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Cited by 112 (5 self)
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Aloha is perhaps the simplest and moststudied medium access control protocol in existence. Only in the recent past, however, have researchers begun to study the performance of Aloha in the presence of selfish users. In this paper, we present a gametheoretic model of multipacket slotted Aloha with perfect information. We show that this model must have an equilibrium and we characterize this equilibrium. Using the tools of stochastic processes, we then establish the equilibrium stability region for some wellknown channel models.
Simple Search Methods for Finding a Nash Equilibrium
 Games and Economic Behavior
, 2004
"... We present two simple search methods for computing a sample Nash equilibrium in a normalform game: one for 2player games and one for nplayer games. We test these algorithms on many classes of games, and show that they perform well against the state of the art the LemkeHowson algorithm for ..."
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Cited by 111 (3 self)
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We present two simple search methods for computing a sample Nash equilibrium in a normalform game: one for 2player games and one for nplayer games. We test these algorithms on many classes of games, and show that they perform well against the state of the art the LemkeHowson algorithm for 2player games, and Simplicial Subdivision and GovindanWilson for nplayer games.