This paper considers a model of society 𝒮 with a finite number of individuals, n, a finite set off alternative, ¦[, effective coalitions that must contain an a priori given number q of individuals. Its purpose is to extend the Nakamura Theorem to the quota games where individuals are allowed to form groups of size q which are smaller than the grand coalition. The present main result determines the upper bound on the number of alternatives which would guarantee, for a given n and q, the existence of a stable coalition structure for any profile of complete transitive preference relations. The notion of stability, 𝒮-equilibrium, introduced by Greenberg-Weber, combines both free entry and free mobility and represents the natural extension of the core to improper or non-cooperative games where coalition structures, and not only the grand coalition, are allowed to form.
