Abstract
This paper considers a model of society\(S\) with a finite number of individuals,n, a finite set off alternatives, Ω effective coalitions that must contain ana priori given numberq of individuals. Its purpose is to extend the Nakamura Theorem (1979) to the quota games where individuals are allowed to form groups of sizeq 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 e andq, the existence of a stable coalition structure for any profile of complete transitive preference relations. Our notion of stability,\(S\)-equilibrium, introduced by Greenberg-Weber (1993), combines bothfree entry andfree 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.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
References
Aumann RJ, Dreze JH (1974) Cooperative games with coalition structures. International Journal of Game Theory 3: 217–237
Balinski M (1970) On the maximum matching, minimal covering. In: Kuhn HW (ed) Proceedings of the Princeton Symposium on Mathematical Programming. Princeton NJ, Princeton University Press
Bondareva ON (1962) Theory of the core of then-person game (in Russian). Vestnik Leningradskogo Universiteta 13: 141–142
Caplin A, Nalebuff B (1992) Individuals and institutions, American Economic Review (Papers and Proceedings) 82: 317–322
Greenberg J, Weber S (1986) Strong tiebout equilibrium under restricted preferences domain. Journal of Economic Theory. 38: 101–117
Greenberg J, Weber S (1993) Stable coalition structures with unidimensional set of alternatives. Journal of Economic Theory. 60: 62–82
Le Breton M (1989) A note on balancedness and nonemptiness of the core in voting games. International Journal of Game Theory. 18: 111–117
Moulin H (1988) Axioms of cooperative decision making. Econometric Society Monographs 15. Cambridge University Press
Nakamura K (1979) The vetoers in simple game with ordinal preferences. International Journal of Game Theory. 8:55–61
Scarf H (1967) The core of ann-person game. Econometrica 35: 50–69
Shapley LS (1972) On balanced sets and cores. Naval Logistics Quarterly 14:453–460
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Deb, R., Weber, S. & Winter, E. The Nakamura Theorem for coalition structures of quota games. Int J Game Theory 25, 189–198 (1996). https://doi.org/10.1007/BF01247101
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01247101