Stable partitions for games with non-transferable utility and externalities

We provide a model of coalitional bargaining with claims in order to solve games with non-transferable utilities and externalities. We show that, for each such game, payoff configurations exist which will not be renegotiated. In the ordinal game derived from these payoff configurations, we can find a partition in which no group of players has an incentive to jointly change their coalitions. For games without externalities this partition and the corresponding payoffs constitute a strong Nash equilibrium in a strategic form game with complete information. We use our model to provide a common framework for a variety of solutions for cooperative games, bargaining problems, and bankruptcy problems.