Simple local search problems that are hard to solve
SIAM Journal on Computing
Journal of Graph Theory
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth 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
The influence of neighbourhood and choice on the complexity of finding pure Nash equilibria
Information Processing Letters
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The complexity of computing a Nash equilibrium
Communications of the ACM - Inspiring Women in Computing
Symmetries and the complexity of pure Nash equilibrium
Journal of Computer and System Sciences
Equilibria of Graphical Games with Symmetries
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games
Proceedings of the 11th ACM conference on Electronic commerce
Pure nash equilibria in games with a large number of actions
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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We study the complexity of computing Nash equilibria in games where players arranged as the vertices of a graph play a symmetric 2-player game against their neighbours. We call this a pairwiseinteraction game. We analyse this game for n players with a fixed number of actions and show that (1) a mixed Nash equilibrium can be computed in constant time for any game, (2) a pure Nash equilibrium can be computed through Nash dynamics in polynomial time for games with a symmetrisable payoff matrix, (3) determining whether a pure Nash equilibrium exists for zero-sum games is NP-complete, and (4) counting pure Nash equilibria is #P-complete even for 2-strategy games. In proving (3), we define a new defective graph colouring problem called Nash colouring, which is of independent interest, and prove that its decision version is NP-complete. Finally, we show that pairwise-interaction games form a proper subclass of the usual graphical games.