Coalition formation with heterogeneous agents

Abstract

When heterogeneous individuals form groups in order to carry out productive activities, equal sharing of surplus implies to loss of efficiency due the trade-off between size or homogeneity each coalition faces. Such loss in efficiency can be mitigated by deviating from equal sharing, e.g., the proportional sharing rule. We show that, under proportional sharing rule, there is a unique stable and efficient coalition structure, which is the grand coalition. We then find conditions under which smaller coalitions can form a constrained efficient and stable coalition structure. We show that such exogenous bounds on coalition size can be endogenized by introducing individualized expansion costs. When such costs implies proportional cost sharing, there is an efficient and stable structure. Finally, we consider a convex combination of the equal and proportional sharing rules, under which individual optimum size may vary non-monotonically with respect to ability.