Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Multi-agent algorithms for solving graphical games
Eighteenth national conference on Artificial intelligence
Universality of Nash Equilibria
Mathematics of Operations Research
Computing correlated equilibria in multi-player games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Computing equilibria in multi-player games
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
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
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
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing good nash equilibria in graphical games
Proceedings of the 8th ACM conference on Electronic commerce
A continuation method for Nash equilibria in structured games
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Complexity results about Nash equilibria
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Computing good nash equilibria in graphical games
Proceedings of the 8th ACM conference on Electronic commerce
How hard is it to approximate the best Nash equilibrium?
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Equilibria of Graphical Games with Symmetries
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On the complexity of constrained Nash equilibria in graphical games
Theoretical Computer Science
Equilibria of graphical games with symmetries
Theoretical Computer Science
Neighbourhood structure in large games
Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge
How Hard Is It to Approximate the Best Nash Equilibrium?
SIAM Journal on Computing
Hi-index | 0.00 |
This paper addresses the problem of fair equilibrium selection in graphical games. Our approach is based on the data structure called the best response policy, which was proposed by Kearns et al. [13] as a way to represent all Nash equilibria of a graphical game. In [9], it was shown that the best response policy has polynomial size as long as the underlying graph is a path. In this paper, we show that if the underlying graph is abounded-degree tree and the best response policy has polynomial size then there is an efficient algorithm which constructs a Nash equilibrium that guarantees certain payoffs to all participants. Another attractive solution concept is a Nash equilibrium that maximizes the social welfare. We show that, while exactly computing the latter is infeasible (we prove that solving this problem may involve algebraic numbers of an arbitrarily high degree), there exists an FPTAS for finding such an equilibrium as long as the best response policy has polynomial size. These two algorithms can be combined to produce Nash equilibria that satisfy various fairness criteria.