International Journal of Game Theory

, Volume 2, Issue 1, pp 235–250

Oddness of the number of equilibrium points: A new proof

  • J. C. Harsanyi

DOI: 10.1007/BF01737572

Cite this article as:
Harsanyi, J.C. Int J Game Theory (1973) 2: 235. doi:10.1007/BF01737572


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 size, those “exceptional” games which fail to satisfy the theorem (by having an even number or an infinity of equilibrium points) is a closed set of measure zero.

Copyright information

© Physica-Verlag Rudolf Liebing KG 1973

Authors and Affiliations

  • J. C. Harsanyi
    • 1
  1. 1.University of CaliforniaBerkeley