Oddness of the number of equilibrium points: A new proof

  title={Oddness of the number of equilibrium points: A new proof},
  author={John C. Harsanyi},
  journal={International Journal of Game Theory},
  • J. Harsanyi
  • Published 1 December 1973
  • Mathematics, Economics
  • International Journal of Game Theory
A new proof is offered for the theorem that, in “almost all” finite games, the number of equilibrium points isfinite andodd. The proof is based on constructing a one-parameter family of games with logarithmic payoff functions, and studying the topological properties of the graph of a certain algebraic function, related to the graph of the set of equilibrium points for the games belonging to this family. In the last section of the paper, it is shown that, in the space of all games of a given… 

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