Group economies and games ∗

We consider an economy in which agents have a preference relation over groups and only over groups. In the economy, each individuals strategy set is a list of those groups containing himself that he would like to form. It is assumed that proposing a group can be made by any single agent, without consent of the other agents involved, therefore in choosing a strategy, an agent is not constrained by the preferences or strategies of other individuals. The realization of groups will depend however on the group proposals of all individuals. We associate our model of group economies with a noncooperative game in strategic form and examine the notions of Nash equilibrium and strong Nash equilibrium. The main features include: a canonical (but very stylized) model to deal with group formation; equivalence results between the core of a group economy and the set of strong Nash equilibria of the associated strategic game; a new look at the standard notion of core-partition of a hedonic game. ∗Preliminary version. Please do not quote. †The University of Kansas, Department of Economics, Lawrence, KS, USA. [email protected]. The author gratefully acknowledges the financial support from the Generalitat de Catalunya, Department d’Universitats, Recerca i Societat de la Informaciò, through grants 2005SGR-00454 and 2005SGR-00836 and the Barcelona Economics Program (XREA). ‡Vanderbilt University & University of Warwick, 2301 Vanderbilt Place, Nashville, USA. [email protected]