This paper presents a new lower bound of 2.414d/√d on the maximal number of Nash equilibria in d × d bimatrix games, a central concept in game theory. The proof uses an equivalent formulation of the problem in terms of pairs of polytopes with 2d facets in d-space. It refutes a recent conjecture that 2d - 1 is an upper bound, which was proved for d ≤ 4. The first counterexample is a 6 × 6 game with 75 equilibria. The case d = 5 remains open. The result carries the lower bound closer to the previously known upper bound of 2.6d/√d.
CITATION STYLE
Von Stengel, B. (1999). New maximal numbers of equilibria in bimatrix games. Discrete and Computational Geometry, 21(4), 557–568. https://doi.org/10.1007/PL00009438
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