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Journal of Optimization Theory and Applications

, Volume 87, Issue 2, pp 419–439 | Cite as

On the probability of existence of pure equilibria in matrix games

  • G. P. Papavassilopoulos
Contributed Papers

Abstract

We examine the probability that a randomly chosen matrix game admits pure equilibria and its behavior as the number of actions of the players or the number of players increases. We show that, for zero-sum games, the probability of having pure equilibria goes to zero as the number of actions goes to infinity, but it goes to a nonzero constant for a two-player game. For many-player games, if the number of players goes to infinity, the probability of existence of pure equilibria goes to zero even if the number of actions does not go to infinity.

Key Words

Matrix games pure equilibria mixed equilibria 

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References

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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • G. P. Papavassilopoulos
    • 1
  1. 1.Department of Electrical Engineering-SystemsUniversity of Southern CaliforniaLos Angeles

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