Two essays on the economics of imperfect information
Two essays on the economics of imperfect information
Run the GAMUT: A Comprehensive Approach to Evaluating Game-Theoretic Algorithms
AAMAS '04 Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems - Volume 2
Reducibility among equilibrium problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The complexity of computing a Nash equilibrium
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Algorithmic Game Theory
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations
Mixed-integer programming methods for finding Nash equilibria
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Local search techniques for computing equilibria in two-player general-sum strategic-form games
Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems: volume 1 - Volume 1
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Since the existence of at least one mixed Nash equilibrium (NE) for any game was proved by Nash, finding NE has been an important issue in the field of game theory. However, polynomial-time algorithms for such task have not yet been discovered, and one of the difficulties is the infinite search space. In this paper, we define the so-called ε-representative strategy to reduce the search space. In general, the equilibria on these representative strategies are not the original equilibria but approximations.To find such approximate equilibria, we then propose a two-level method, which firstly uses co-evolutionary algorithms to co-evolve the representative strategies for each player and then the approximate equilibria.The computational time can be controlled by the parameters of the co-evolutionary algorithms. Empirical results show that our method finds the approximate NE in a reasonable time. Finally, the definitions developed in this paper help define the co-evolvability of NE.