Computing equilibria: a computational complexity perspective

Roughgarden, Tim

doi:10.1007/s00199-009-0448-y

Cited by 54 publications

(46 citation statements)

References 132 publications

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“…In a spectacular sequence of papers (summarized in Daskalakis, Goldberg, andPapadimitriou 2006, andChen andDeng 2006), it was recently shown that this problem is "PPAD-complete", that is, in a certain sense "as hard" as solving many other, seemingly harder, problems related to equilibria, for example finding an approximate fixed point of a Brouwer function. In his contribution, Roughgarden (2010) explains this result and many others.…”

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confidence: 63%

“…This is important, for example, for applications in artificial intelligence where a poker playing program should exploit mistakes of an opponent who does not play optimally. Tim Roughgarden's survey (Roughgarden 2010) is directed at readers with a background in economics. Computational complexity deals with the intrinsic difficulty of solving a computational problem.…”

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confidence: 99%

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Computation of Nash equilibria in finite games: introduction to the symposium

Stengel

2009

Econ Theory

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) are longer surveys, the others present new research. All contributions attempt to make the material accessible and interesting to the non-specialist. The collection reflects in equal measure the state of research, as well as providing an exposition of the main ideas and questions of the field. The articles are also bridged by a unity of ideas that appear in many places.The topic of this collection is a computational problem: given a game in some finite description, find its Nash equilibria; or, a more modest task: find one Nash equilibrium of the game. These questions pose highly interesting challenges for economics, mathematics, and computer science.For the applied economist, noncooperative games are a modeling tool, with the Nash equilibrium as the central solution concept. Interpreting and discussing a Nash equilibrium is essential for the model, but the equilibrium has to be found first, which often takes a substantial amount of the analysis. A computer program for this analysis should save time and allow for more detailed modeling.Why should the applied economist, as a modeler and user of game theory, care about algorithms? It seems easy just to convert the equilibrium problem to a suitable optimization problem, run some mathematical software on it, and use the solution. The problem is that such a "black box algorithm" is unlikely to work on all but the smallest cases. Any algorithm that "scales" reasonably well in allowing for more detailed games as input, and still finishes in reasonable time, must exploit the mathematical structure of the problem.

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confidence: 63%

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confidence: 99%

Computation of Nash equilibria in finite games: introduction to the symposium

Stengel

2009

Econ Theory

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“…However, new results suggest that there is no general polynomial time approximation scheme for computing a Nash equilibrium [10]. For recent surveys on the problem of computing Nash equilibria, one can refer to [14,42]. A comprehensive survey of various methods of computing Nash equilibria and their computational complexity results are given in [34].…”

Section: Rational Interactions and Strategic Equilibriummentioning

confidence: 98%

Applications of Algebra for Some Game Theoretic Problems

Gandhi

Chatterji

2015

Int. J. Found. Comput. Sci.

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In this paper we present applications of polynomial algebra for the problem of computing Nash equilibria of a subclass of finite normal form games. We characterize Nash equilibria of a normal form game as solutions to a system of polynomial equations and define the subclass of games under consideration. We present an algebraic method for deciding membership decision to the subclass of games. A method based on group action to compute all Nash equilibria of the subclass of games is presented with examples to show working of the methods. We also present some related results and discuss properties of the subclass of games.

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“…We then discuss the key differences between the two settings. For work on the complexity of computing other equilibrium concepts, such as market, correlated, and approximate Nash equilibria, and for a discussion of equilibrium computation in extensive-form, compact, randomly generated, and stochastic games, see [30, Part I] and [38] and the references therein.…”

Section: Complexity Of Equilibrium Computationmentioning

confidence: 99%

Algorithmic Game Theory

Persiano¹

2011

Lecture Notes in Computer Science

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Computing equilibria: a computational complexity perspective

Cited by 54 publications

References 132 publications

Computation of Nash equilibria in finite games: introduction to the symposium

Computation of Nash equilibria in finite games: introduction to the symposium

Applications of Algebra for Some Game Theoretic Problems

Algorithmic Game Theory

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