Coalitional bargaining with consistent counterfactuals

We propose a new solution concept for TU cooperative games in characteristic function form, the SCOOP, which builds on the symmetric Nash Bargaining Solution (NBS) by adding a consistency requirement for negotiations inside every coalition. The SCOOP specifies the probability of success and the payoffs to each coalition. The players share the surplus of a coalition according to the NBS. The disagreement payoffs are computed as the expectation of payoffs in other coalitions, using a common probability distribution that is derived from the prior distribution. The predicted outcome can be probabilistic or deterministic, but only an efficient coalition can succeed with probability one. We discuss the necessary and sufficient conditions for an efficient solution. In either case, the SCOOP always exists, is generically unique for superadditive games, and is easy to compute. Moreover, in the spirit of the Nash program, we propose a non-cooperative protocol whose stationary equilibrium identifies the SCOOP as the limit equilibrium outcome.