On the Existence of Nash Equilibria in Discontinuous and Qualitative Games

  title={On the Existence of Nash Equilibria in Discontinuous and Qualitative Games},
  author={Paulo Barelli and IDIONE SOZA},
We show that compact games have pure strategy Nash equilibria if conditions C and Q are satisfied. Condition C states that, whenever a profile of strategies x is not an equilibrium, there exists an open neighborhood V of x and well behaved maps φi, one for each player i, mapping V to each player’s strategies, and satisfying the following property: for any profile of strategies y in the neighborhood V , there exists one player i such that φi(y) belongs to player i’s strict upper contour set… CONTINUE READING
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