Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Nash equilibria in graphical games on trees revisited
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Discretized Multinomial Distributions and Nash Equilibria in Anonymous Games
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Artificial Intelligence
Approximate Nash Equilibria for Multi-player Games
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
An Efficient PTAS for Two-Strategy Anonymous Games
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
On oblivious PTAS's for nash equilibrium
Proceedings of the forty-first annual ACM symposium on Theory of computing
On a Network Generalization of the Minmax Theorem
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Ranking games that have competitiveness-based strategies
Proceedings of the 11th ACM conference on Electronic commerce
Approximate well-supported nash equilibria below two-thirds
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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An extensive literature in economics and social science addresses contests, in which players compete to outperform each other on some measurable criterion, often referred to as a player's score, or output. Players incur costs that are an increasing function of score, but receive prizes for obtaining higher score than their competitors. In this paper we study finite games that are discretized contests, and the problems of computing exact and approximate Nash equilibria. Our motivation is the worst-case hardness of Nash equilibrium computation, and the resulting interest in important classes of games that admit polynomial-time algorithms. For games that have a tie-breaking rule for players' scores, we present a polynomial-time algorithm for computing an exact equilibrium in the 2-player case, and for multiple players, a characterization of Nash equilibria that shows an interesting parallel between these games and unrestricted 2-player games in normal form. When ties are allowed, via a reduction from these games to a subclass of anonymous games, we give approximation schemes for two special cases: constant-sized set of strategies, and constant number of players.