Some optimal inapproximability results
Journal of the ACM (JACM)
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing pure nash equilibria in graphical games via markov random fields
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Nash equilibria in graphical games on trees revisited
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Progress in approximate nash equilibria
Proceedings of the 8th ACM conference on Electronic commerce
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A constructive proof of the Lovász local lemma
Proceedings of the forty-first annual ACM symposium on Theory of computing
Graphical models for game theory
UAI'01 Proceedings of the Seventeenth conference on Uncertainty in artificial intelligence
On approximate nash equilibria in network design
WINE'10 Proceedings of the 6th international conference on Internet and network economics
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In many types of games, mixed Nash equilibria is not a satisfying solution concept, as mixed actions are hard to interpret. However, pure Nash equilibria, which are more natural, may not exist in many games. In this paper we explore a class of graphical games, where each player has a set of possible decisions to make, and the decisions have bounded interaction with one another. In our class of games, we show that while pure Nash equilibria may not exist, there is always a pure approximate Nash equilibrium. We also show that such an approximate Nash equilibrium can be found in polynomial time. Our proof is based on the Lovász local lemma and Talagrand inequality, a proof technique that can be useful in showing similar existence results for pure (approximate) Nash equilibria also in other classes of games.