The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Efficient Computation of Approximate Pure Nash Equilibria in Congestion Games
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Proceedings of the 13th ACM Conference on Electronic Commerce
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Among other solution concepts, the notion of the pure Nash equilibrium plays a central role in Game Theory. Pure Nash equilibria in a game characterize situations with non-cooperative deterministic players in which no player has any incentive to unilaterally deviate from the current situation in order to achieve a higher payoff. Unfortunately, it is well known that there are games that do not have pure Nash equilibria. Furhermore, even in games where the existence of equilibria is guaranteed, their computation can be a computationally hard task. Such negative results significantly question the importance of pure Nash equilibria as solution concepts that characterize the behavior of rational players. Approximate pure Nash equilibria, which characterize situations where no player can significantly improve her payoff by unilaterally deviating from her current strategy, could serve as alternative solution concepts provided that they exist and can be computed efficiently. In this letter, we discuss recent positive algorithmic results for approximate pure Nash equilibria in congestion games.