The complexity of decision problems about nash equilibria in win-lose games

Authors:
Vittorio Bilò;Marios Mavronicolas
Affiliations:
Department of Mathematics and Physics ”Ennio De Giorgi”, University of Salento, Lecce, Italy;Department of Computer Science, University of Cyprus, Nicosia, Cyprus
Venue:
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Year:
2012

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Abstract

We revisit the complexity of deciding, given a (finite) strategic game, whether Nash equilibria with certain natural properties exist; such decision problems are well-known to be $\cal NP$-complete [2, 6, 10] . We show that this complexity remains unchanged when all utilities are restricted to be 0 or 1; thus, win-lose games are as complex as general games with respect to such decision problems.