Equilibria in a model with partial rivalry

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 satisfy independence of irrelevant choices, anonymity, and partial rivalry. Moreover, if any of these assumptions is violated, then even a pure strategy Nash equilibrium may fail to exist. Furthermore, 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. (C) 1997 Academic Press.