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Inapproximability of pure Nash equilibria
 IN PROCEEDINGS OF THE 40TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING (STOC
, 2008
"... Purestrategy Nash equilibria are a natural and convincing solution concept for multiplayer games with the finite improvement property, i.e., any sequence of improvement steps by individual players is finite and any maximal such sequence terminates in a Nash equilibrium. By far the most literature a ..."
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Cited by 32 (2 self)
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the finite improvement property is guaranteed by an exact potential function. The complexity of computing pure Nash equilibria in congestion games was recently shown to be PLScomplete. In this paper, we therefore study the complexity of computing approximate equilibria in congestion games. An αapproximate
Algorithms for approximating Nash equilibria
 IN: PROCEEDINGS OF THE 2ND WORKSHOP ON INTERNET AND NETWORK ECONOMICS (WINE’06
, 2006
"... 1 PROBLEM DEFINITION Nash [13] introduced the concept of Nash equilibria in noncooperative games and proved that any game possesses at least one such equilibrium. A wellknown algorithm for computing a Nash equilibrium of a 2player game is the LemkeHowson algorithm [11], however it has exponentia ..."
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Cited by 26 (5 self)
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[2] proved that the problem is PPADcomplete for 2player games as well. This fact emerged the computation of approximate Nash equilibria. There are several versions of approximate Nash equilibria that have been defined in the literature; however the focus of this entry is on the notions of ɛNash
Approximate Nash Equilibria in Anonymous Games
, 2014
"... We study from an algorithmic viewpoint anonymous games [Mil96, Blo99, Blo05, Kal05]. In these games a large population of players shares the same strategy set and, while players may have different payoff functions, the payoff of each depends on her own choice of strategy and the number of the other ..."
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Cited by 3 (1 self)
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players playing each strategy (not the identity of these players). We show that, the intractability results of [DGP09a] and [Das11] for general games notwithstanding, approximate mixed Nash equilibria in anonymous games can be computed in polynomial time, for any desired quality of the approximation
Approximate Nash Equilibria for Multiplayer Games
"... We consider games of complete information with r ≥ 2 players, and study approximate Nash equilibria in the additive and multiplicative sense, where the number of pure strategies of the players is n. We establish a lower bound of r−1 ln n−2 ln ln n−ln r on the size of the support of strategy profil ..."
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Cited by 9 (0 self)
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We consider games of complete information with r ≥ 2 players, and study approximate Nash equilibria in the additive and multiplicative sense, where the number of pure strategies of the players is n. We establish a lower bound of r−1 ln n−2 ln ln n−ln r on the size of the support of strategy
Computing equilibria in anonymous games
 in 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS
, 2007
"... We present efficient approximation algorithms for finding Nash equilibria in anonymous games, that is, games in which the players utilities, though different, do not differentiate between other players. Our results pertain to such games with many players but few strategies. We show that any such gam ..."
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Cited by 35 (5 self)
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such game has an approximate pure Nash equilibrium, computable in polynomial time, with approximation O(s 2 λ), where s is the number of strategies and λ is the Lipschitz constant of the utilities. Finally, we show that there is a PTAS for finding an ɛapproximate Nash equilibrium when the number
Computing pure Nash and strong equilibria in bottleneck congestion games
 IN PROC. 18TH EUROPEAN SYMPOSIUM ON ALGORITHMS (ESA
, 2010
"... Bottleneck congestion games properly model the properties of many realworld network routing applications. They are known to possess strong equilibria – a strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, westudy the computational complexity of pure Nash ..."
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Cited by 5 (2 self)
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Bottleneck congestion games properly model the properties of many realworld network routing applications. They are known to possess strong equilibria – a strengthening of Nash equilibrium to resilience against coalitional deviations. In this paper, westudy the computational complexity of pure Nash
Approximate and wellsupported approximate Nash equilibria of random bimatrix games
 IN PROCEEDINGS OF THE 11TH PANHELLENIC CONFERENCE ON INFORMATICS (PCI 2007
, 2007
"... We focus on the problem of computing approximate Nash equilibria and wellsupported approximate Nash equilibria in random bimatrix games, where each player’s payoffs are bounded and independent random variables, not necessarily identically distributed, but with common expectations. We show that the ..."
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Cited by 1 (0 self)
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We focus on the problem of computing approximate Nash equilibria and wellsupported approximate Nash equilibria in random bimatrix games, where each player’s payoffs are bounded and independent random variables, not necessarily identically distributed, but with common expectations. We show
On the complexity of Nash equilibria of ActionGraph Games
 In SODA: Proceedings of the ACMSIAM Symposium on Discrete Algorithms
, 2009
"... In light of much recent interest in finding a model of multiplayer multiaction games that allows for efficient computation of Nash equilibria yet remains as expressive as possible, we investigate the computational complexity of Nash equilibria in the recently proposed model of actiongraph games (A ..."
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Cited by 7 (1 self)
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In light of much recent interest in finding a model of multiplayer multiaction games that allows for efficient computation of Nash equilibria yet remains as expressive as possible, we investigate the computational complexity of Nash equilibria in the recently proposed model of actiongraph games
Approximating Pure Nash Equilibrium in Cut, Party Affiliation, and Satisfiability Games
"... Cut games and party affiliation games are wellknown classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLScom ..."
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Cited by 12 (1 self)
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Cut games and party affiliation games are wellknown classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLS
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