Hedonic Coalitions: Optimality and Stability

Abstract

In many economic situations, individuals carry out activities as coalitions, and have personal preferences for belonging to specific groups (coalitions). These situations are studied in the framework of cooperative games with coalition structures, by defining for each player a utility function with two arguments, namely his consumption bundle and the coalition to which (s)he belongs. The optimality analysis brings out a surprising property of the games with coalitions, namely that transfers among coalitions may be necessary to attain Pareto optimality. Moreover, quite restrictive assumptions are needed to rule out this property. The analysis is concerned with the conditions under which no has incentives and opportunities to change Two concepts of individual stability of a coalition structure are introduced, and their existence properties are analyzed. 1.1 Summary IN MANY ECONOMIC SITUATIONS, individuals carry out activities as Thus, individuals organize themselves in firms for production purposes and in clubs for consumption purposes; or they rely upon local communities for the provision of public goods. In such situations, individuals typically have personal preferences for belonging to specific groups (coalitions). First, they are concerned with the size of the group and personalities of its members. Second, they are concerned with qualitative and quantitative characteristics of the group activities: Working conditions in the firms, facilities available at the clubs, local public goods. Cooperative games with coalition structures provide a natural framework for a formal analysis of these situations, when the individuals partition themselves into A general way of introducing explicitly personal preferences for membership in specific coalitions is to define for each player a utility function with two arguments, namely his consumption bundle and the coalition to which he belongs. It then seems natural to speak about games with hedonic coalitions. A model of an economy, or cooperative game, with coalitions is introduced in Section 1.2. The agents organize themselves in coalitions which form a partition (i.e., each agent belongs to one and only one coalition). Each coalition, endowed with a production set, produces public and private goods. Each agent consumes the public goods produced by the coalition to which he belongs, and private goods. His preferences are represented by a utility function which is strictly increasing in private goods and continuous in private as well as public goods, but which depends upon the coalition in an arbitrary way. Our initial interest was to study the of coalitions in this model. Section 3 is devoted to that topic. However, in the course of our study, we encountered an