Stable Coalition Structures with Fixed Decision Scheme

Abstract

This paper studies the stability of coalition structures when coalitions must choose an alternative in a one-dimensional space, using a fixed decision scheme. This decision scheme depends on the preferred alternative of all agents in the coalition. We assume that the number of agent is finite. Hence, when an agent, or a group of agent, leaves a coalition and enter in another coalition, this will affect the outcome of the decision scheme in the former and the new coalitions. We provide in this paper sufficient conditions for the existence of stable coalition structures, for two stability concepts, namely C-stability and Tiebout-stability. The model presented here can be understood as a local public good economy with horizontal differentiation.

I wish to thank Salvador Barberà, Marcus Berliant, Carmen Bevià Peirre Dehez, Carmen Herrero, Michel Le Breton, Jean Françis Mertens, Thomas Palfrey, Ulrich Schmidt, Gisèle Umbhauer, Myrna Wooders, seminar audiences at CORE, 1999 “Ecole de Printemps” of CORE-GREQAM in Aix-en-Provence, 2000 Public Economic Theory Conference in Warwick, and 2000 World Congress of the Econometric Society in Seattle for helpful comments and criticisms. I am particularly grateful to Hideo Konishi and Jordi Massó for comments and suggestions that greatly improved the exposition of this work. Part of this work was done while I was visiting the Institute of Mathematical Economics at Bielefeld University under the European research programme “Game-theoretic approaches to cooperation and exchange of information, with economic application.” Financial support from the European Commision, contract number HPMF-CT-1999-00284, is gratefully acknowledge. All remaining errors are mine.