Coalitional games and contracts based on individual deviations

We study what coalitions form and how the members of each coalition split the coalition value in coalitional games in which only individual deviations are allowed. In this context we employ three stability notions: individual, contractual, and compensational stability. These notions differ in terms of the underlying contractual assumptions. We characterize the coalitional games in which individually stable outcomes exist by means of the top‐partition property. Furthermore, we show that any coalition structure of maximum social worth is both contractually and compensationally 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. In addition, we study monotonic simple proper games and establish that any outcome containing a winning coalition is both contractually and compensationally stable. We show that an individually stable outcome containing a winning coalition always exists, and characterize all such outcomes.