Cooperative game under risk and externalities

Abstract

When a group of self-interested players plan to take joint action by cooperating with each other, a fundamental issue arises is to agree upon how to allocate the prospective gain from cooperation among the group members in a way that satisfies everyone involved. Players break away from the group if they are not satisfied with the allocation. In this paper, we propose a solution to this issue under a situation when the prospective gain is: (i) risky because participating players are uncertain or ignorant about whether every group member is capable of performing an action or will indeed take an action that benefits the group; and (ii) under externalities because the group can also benefit or lose from some external events or the activities of other players not in the group. To address this issue, we propose a cooperative game model in stochastic partition function form. We propose a solution concept called foresighted nucleolus which characterizes an equitable allocation of payoffs based on the notion of inequity aversion. Players do not break away from the group if the allocation lies in the foresighted nucleolus. We provide a computational method for determining the allocation. Results show that the foresighted nucleolus always exists, but it may not be unique.