We investigate from the computational viewpoint multi-player games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLS-complete in general. We discuss implications to non-atomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.
['Alex Fabrikant', 'Christos H. Papadimitriou', 'Kunal Talwar']
The complexity of pure Nash equilibria