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Published August 30, 2017 | Submitted
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The Maximal Number of Regular Totally Mixed Nash Equilibria


Let S=∏^n_(i=1) Si be the strategy space for a finite n-person game. Let (S10,…, Sn0) ϵ S be any strategy n-tuple, and let Ti = Si - {si0}, i = 1, ..., n. We show that the maximum number of regular totally mixed Nash equilibria to a game with strategy sets Si is the number of partitions P = {P1,…, Pn} of UiTi such that, for each i, #Pi = #Ti and Pi ∩ Ti = ∅. The bound is tight, as we give a method for constructing a game with the maximum number of equilibria.

Additional Information

This research was supported in part by National Science Foundation grants SBR-9308862 to the University of Minnesota and SBR-9308637 to the California Institute of Technology. We benefited from stimulating discussions with Victor Reiner and Michel leBreton. Published as McKelvey, Richard D., and Andrew McLennan. "The maximal number of regular totally mixed Nash equilibria." Journal of Economic Theory 72, no. 2 (1997): 411-425.

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August 20, 2023
August 20, 2023