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Topological degree and number of Nash equilibrium points of bimatrix games

Abstract

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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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

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Key Words

  • Topological degree
  • homotopy
  • Nash equilibrium points
  • bimatrix games
  • players
  • retraction