The Nakamura theorem for coalition structures of quota games

Rajat Deb*, Shlomo Weber, Eyal Winter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Abstract: This paper considers a model of society script capital L sign with a finite number of individuals, n, a finite set off alternatives, Ω, 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 capital L sign-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.

Original languageAmerican English
Pages (from-to)189-198
Number of pages10
JournalInternational Journal of Game Theory
Issue number2
StatePublished - 1996


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