In this paper, using the topological degree, we give a new proof of a well-known result: the number of Nash equilibrium points of a nondegenerate bimatrix game is odd. The calculation of the topological degree allows the localization of the whole set of non-degenerate equilibrium points.
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Nash, J.,Noncooperative Games, Annals of Mathematics, Vol. 54, No. 2, 1951.
Lemke, C. E., andHowson, J. T.,Equilibrium Points of Bimatrix Games, SIAM Journal on Applied Mathematics, Vol. 12, No. 2, 1964.
Schwartz, J. T.,Nonlinear Functional Analysis, Gordon and Breach, New York, New York, 1969.
Todd, M. J.,The Computation of Fixed Points and Applications, Springer-Verlag, Berlin, Germany, 1976.
Erdelsky, P. J.,Computing the Brouwer Degree in R 2, Mathematics of Computation, Vol. 27, No. 121, 1973.
Le Van, C.,Calcul sur Ordinateur de Degré Topologique dans R 2 et R 3, Thèse de 3è Cycle, Université Paris-IX, Dauphine, France, 1978.
O'Neil, T., andThomas, J. W.,The Calculation of Topological Degree by Quadrature, SIAM Journal on Numerical Analysis, Vol. 12, No. 5, 1975.
Communicated by G. Leitmann
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Le Van, C. Topological degree and number of Nash equilibrium points of bimatrix games. J Optim Theory Appl 37, 355–369 (1982). https://doi.org/10.1007/BF00935275
- Topological degree
- Nash equilibrium points
- bimatrix games