Contracts and Coalition Formation based on Individual Deviations

This paper revisits the work of Dreze and Greenberg (1980) in a general context-free environment and studies endogenous coalition formation problems based on three stability notions that reflect three different contractual arrangements with respect to one-person deviations. Analyzing coalition formation within the framework of transferable utility games, we propose to modify the original definitions of these stability notions due to some, in our opinion, unwanted characteristics. To emphasize this difference we re-baptize the stability notions into individual stability, contractual stability, and compensation stability. In particular, with the new definition individual rationality is implied by individual stability. We, furthermore, show that any coalition structure of maximum social worth is both contractually and compensation stable. In addition, we analyze existence and study the relations between the stability notions. We show that an individually stable outcome is also contractually stable and that an individually rational and compensation stable outcome is also contractually stable. Applying the general framework to an example of mutual insurance in production, we find that in each type of contractual setting there are stable individually rational pooling outcomes while, on the contrary, individually rational separating outcomes are not stable in general.