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
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
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
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
Ranking Games and Gambling: When to Quit When You're Ahead
Operations Research
Ranking games that have competitiveness-based strategies
Theoretical Computer Science
Hi-index | 0.00 |
This paper studies - from the perspective of efficient computation - a type of competition that is widespread throughout the plant and animal kingdoms, higher education, politics and artificial contests. In this setting, an agent gains utility from his relative performance (on some measurable criterion) against other agents, as opposed to his absolute performance. We model this situation using ranking games in which each strategy corresponds to a level of competitiveness, and incurs an upfront cost that is higher for more competitive strategies. We study the Nash equilibria of these games, and polynomial-time algorithms for computing them. For games in which there is no tie between agents' levels of competitiveness we give a polynomial-time algorithm for computing an exact equilibrium in the 2-player case, and 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 polynomial-time approximation schemes for two special cases: constant-sized set of strategies, and constant number of players. The latter result is improved to a fully polynomial-time approximation scheme when the constant number of players only compete to win the game, i.e. to be ranked first.