Equilibria in a Model with Partial Rivalry

Abstract

In this paper we show that a non-cooperative game with a finite set of players and common finite strategy sets possesses a strong Nash equilibrium in pure strategies whenever individuals' preferences satisfyindependence of irrelevant choices,anonymity, andpartial rivalry. Moreover, if any of these assumptions is violated, then even a pure strategy Nash equilibrium may fail to exist. Further- more, we demonstrate that even with a continuum of players, the same three assumptions yield the existence of a pure strategy strong Nash equilibrium and, in addition, the equivalence of the sets of Nash and strong Nash equilibria in pure strategies.Journal of Economic LiteratureClassification Numbers: C72, D62.