Agreements with overlapping coalitions

When groups can perform a task more efficiently than single individuals, a desirable behavior is to form coalitions. Coalitions can be disjoint or overlapping. But, almost all the economics literature on coalition formation is mostly restricted to models where coalitions are disjoint. However, in politics, environmental issues, customs unions, informal insurance, and many other economic, social, and political interactions, we observe overlapping coalitions. How can we understand agreements involving overlapping coalitions ? How can we study their efficiency if there is no theory to model them ? My thesis solves these questions by developing a framework on coalition formation that accommodates overlapping coalitions. In the first chapter, following a non-cooperative approach, I develop a bargaining game to model the formation of overlapping coalitions. I show the existence of a subgame perfect equilibrium and I provide an algorithm that generates equilibrium outcomes for symmetric games. I establish an overlapping coalition’s representation for each network and I show that, under some conditions, they are equilibrium outcomes. The core is the most popular solution concept in cooperative game. In the second chapter, following a cooperative approach, I develop a new concept of core that accommodates overlapping coalitions, and coincides with the recursive core when coalitions do not intersect. First, I extend naively the residual game to only embody overlapping coalitions, and I obtain a range of allocations between the optimistic and the pessimistic core. Secondly, I provide a consistent notion of residual game and I show  that the overlapping coalition structure core not only stands as a generalization of the coalition structure core, but also induces a refinement of the extended recursive core. As I build a theoretical framework for overlapping coalition formation, I provide applications in the remainder of the thesis. In the third chapter, I model informal insurance arrangements as a collection of overlapping trust coalitions. The model is based on empirical facts. I enrich the theoretical modeling of informal insurance arrangements by introducing four key features : the merging of the group approach and the network approach, the possibility for informal insurance organizations to overlap, the endogenous punishment scheme, and externalities. I characterize self enforcing stable informal insurance arrangements and I derive conditions under which deviation occurs. While it is always assumed in the literature that only wealthy individuals may deviate. I formally isolate conditions under which this assumption holds. Furthermore, I show that if these conditions does not hold, this assumption is violated. Finally, I provide static comparative results for consumption under two distinct sharing norms. Finally in the fourth chapter, I investigate multilateral informal insurance organizations built on networks of trust relationships. The model is based on empirical findings and nests the traditional approaches which use bilateral links or groups. I characterize self enforcing stable informal insurance organizations without imposing extreme discounting. I show that density and clustering characterize networks that match the lowest discounting for stability. While insurance is formally arranged to smooth consumption, I show that external effects such as social privileges tend to reinforce the stability of such arrangement. I use my stability results to derive comparative statics for exogenous parameters of the model. Finally, I develop a procedure in finite steps that equates consumption for all linked individuals. Contrary to the existing procedures in infinite steps, my procedure is more realistic and useful to policy makers.

Keyphrases: Overlapping coalitions, Networks, Cooperative and non-cooperative games, Core, Stability, Informal insurance, Sharing rules