Coalitional and Chance-Constrained Solutions to n-Person Games, II: Two-Stage Solutions

We extend the theory of n-person cooperative games in characteristic function form to games with stochastic characteristic functions. We propose a payoff process to the players in these games that is composed of two parts. In the first part the players are promised some prior payoffs. In the second part we use the two-stage solution concepts to modify the prior payoffs in a manner acceptable to the players. We verify the existence of these solution concepts and explore some of their properties.