New Lower Bounds for the Number of Equilibria in Bimatrix Games
نویسنده
چکیده
A class of nondegenerate n n bimatrix games is presented that have asymptotically more than 2:414 n = p n Nash equilibria. These are more equilibria than the 2 n ? 1 equilibria of the game where both players have the identity matrix as payoo matrix. This refutes the Quint{Shubik conjecture that the latter number is an upper bound on the number of equilibria of nondegenerate n n games. The rst counterexample is a 6 6 game with 75 equilibria. The approach uses concepts from polytope theory, which imply a known upper bound of 2:6 n = p n.
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