The complexity of uniform Nash equilibria and related regular subgraph problems

We investigate the complexity of finding Nash equilibria in which the strategy of each player is uniform on its support set. We show that, even for a restricted class of win–lose bimatrix games, deciding the existence of such uniform equilibria is an -complete problem. Our proof is graph-theoretical. Motivated by this result, we also give -completeness results for the problems of finding regular induced subgraphs of large size or regularity, which can be of independent interest.