This paper considers a model of society [script S] with a finite number of individuals, n, a finite set off alternatives, Omega, effective coalitions that must contain an a priori given number q of individuals. Its purpose is to extend the Nakamura Theorem (1979) to the quota games where individuals are allowed to form groups of size q which are smaller than the grand coalition. Our 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. Our notion of stability, [script S]-equilibrium, introduced by Greenberg-Weber (1993), combines both free entry and free mobility and represents the natural extension of the core to improper or non-superadditive games where coalition structures, and not only the grand coalition, are allowed to form.
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