Finding a Nash Equilibrium in Spatial Games is an NP-Complete Problem

Abstract

We consider the class of (finite) spatial games. We show that the problem of determining whether there exists a Nash equilibrium in which each player has a payoff of at least k is NP-complete as a function of the number of players. When each player has two strategies and the base game is an anti-coordination game, the problem is decidable in polynomial time.spatial games; NP-completeness; graph K-colorability