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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 172 (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.
Computing Equilibria in MultiPlayer Games
 In Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... We initiate the systematic study of algorithmic issues involved in finding equilibria (Nash and correlated) in games with a large number of players; such games, in order to be computationally meaningful, must be presented in some succinct, gamespecific way. We develop a general framework for obta ..."
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Cited by 54 (4 self)
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We initiate the systematic study of algorithmic issues involved in finding equilibria (Nash and correlated) in games with a large number of players; such games, in order to be computationally meaningful, must be presented in some succinct, gamespecific way. We develop a general framework for obtaining polynomialtime algorithms for optimizing over correlated equilibria in such settings, and show how it can be applied successfully to symmetric games (for which we actually find an exact polytopal characterization), graphical games, and congestion games, among others. We also present complexity results implying that such algorithms are not possible in certain other such games. Finally, we present a polynomialtime algorithm, based on quantifier elimination, for finding a Nash equilibrium in symmetric games when the number of strategies is relatively small.
Complexity of Iterated Dominance and a New Definition of Eliminability
, 2004
"... While the Nash equilibrium solution concept is studied more and more intensely in our community, the perhaps more elementary concept of iterated dominance has received much less attention. This paper makes two main contributions. First, we prove ..."
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While the Nash equilibrium solution concept is studied more and more intensely in our community, the perhaps more elementary concept of iterated dominance has received much less attention. This paper makes two main contributions. First, we prove
Theory
"... 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 ..."
Abstract
 Add to MetaCart
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.