Abstract
We are interested in the complexity of finding Nash equilibria with one uniformly mixed strategy (that is, equilibria in which at least one of the players plays a uniform probability distribution over some set of pure strategies). We show that, even in imitation bimatrix games, where one player has a positive payoff if he plays the same pure strategy as the opponent, deciding the existence of such an equilibrium is an NP-complete problem. We derive this result from the NP-completeness of graph-theoretical problems strictly related to this class of equilibria.
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Bonifaci, V., Di Iorio, U., Laura, L. (2005). New Results on the Complexity of Uniformly Mixed Nash Equilibria. In: Deng, X., Ye, Y. (eds) Internet and Network Economics. WINE 2005. Lecture Notes in Computer Science, vol 3828. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11600930_103
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DOI: https://doi.org/10.1007/11600930_103
Publisher Name: Springer, Berlin, Heidelberg
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