The complexity of uniform Nash equilibria and related regular subgraph problems

14 years 10 days ago

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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 NP-complete problem. Our proof is graph-theoretical. Motivated by this result, we also give NP-completeness results for the problems of finding regular induced subgraphs of large size or regularity, which can be of independent interest. Key words: computational complexity, NP-completeness, uniform Nash equilibrium, regular induced subgraph

Vincenzo Bonifaci, Ugo Di Iorio, Luigi Laura

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