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 equil ibrium in pure strategies whenever individuals' preferences satisfy in dependence of irrelevant choices, anonymity, and partial rivalry. More over, if any of these assumptions is violated, then even a pure strate gy Nash equilibrium may fail to exist. Furthermore, we demonstrate tha t even with a continuum of players, the same three assumptions yield t he existence of a pure strategy strong Nash equilibrium and, in additi on, the equivalence of the sets of Nash and strong Nash equilibria in pure strategies. (C) 1997 Academic Press.