Symmetry and p-Stability

A symmetry of a game is a permutation of the player set and their strategy sets that leaves the payoff functions invariant. In this paper we introduce and discuss two relatively mild symmetry properties for set-valued solution concepts (that are equivalent when the solution concepts are singlevalued) and show using examples that stable sets satisfy neither version. These examples also show that for every integer q, there exists a game with an equilibrium component of index q.