On stability of coalitions when externalities and stochasticity co-exist

Abstract

We consider a class of cooperative games with transferable utilities where the payoff to a coalition is a function of the overall coalition structure (externalities) and the payoff to a coalition is not deterministic (stochasticity). Externalities and stochasticity in the cooperative game theory literature have almost always been studied separately. We propose a theoretical framework to analyze a situation when both are present together. We introduce a notion of stability and propose a related solution concept, called “foresighted nucleolus”. We prove that the foresighted nucleolus always exists, but it may not be unique. We also provide a computational method and a numerical example to illustrate the solution concept.