Journal of the ACM (JACM)
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth 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
The computational complexity of nash equilibria in concisely represented games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
The influence of neighbourhood and choice on the complexity of finding pure Nash equilibria
Information Processing Letters
Computing good nash equilibria in graphical games
Proceedings of the 8th ACM conference on Electronic commerce
Computing Equilibria in Anonymous Games
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
Pure Nash equilibria: hard and easy games
Journal of Artificial Intelligence Research
The complexity of games on highly regular graphs
ESA'05 Proceedings of the 13th annual European conference on Algorithms
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We study graphical games where the payoff function of each player satisfies one of four types of symmetry in the actions of his neighbors. We establish that deciding the existence of a pure Nash equilibrium is NP-hard in general for all four types. Using a characterization of games with pure equilibria in terms of even cycles in the neighborhood graph, as well as a connection to a generalized satisfiability problem, we identify tractable subclasses of the games satisfying the most restrictive type of symmetry. Hardness for a different subclass leads us to identify a satisfiability problem that remains NP-hard in the presence of a matching, a result that may be of independent interest. Finally, games with symmetries of two of the four types are shown to possess a symmetric mixed equilibrium which can be computed in polynomial time. We thus obtain a natural class of games where the pure equilibrium problem is computationally harder than the mixed equilibrium problem, unless P=NP.