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.
This work was partially supported by “Progetto 5 per mille per la ricerca”: “Collisioni fra vortici puntiformi e fra filamenti di vorticità: singolarità, trasporto e caos” at the University of Salento and by research funds at the University of Cyprus.
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Bilò, V., Mavronicolas, M. (2012). The Complexity of Decision Problems about Nash Equilibria in Win-Lose Games. In: Serna, M. (eds) Algorithmic Game Theory. SAGT 2012. Lecture Notes in Computer Science, vol 7615. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33996-7_4
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DOI: https://doi.org/10.1007/978-3-642-33996-7_4
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