(with Rajiv Vohra). April 2025, revised August 2026. Supplementary Notes.
Summary. We revisit Nash’s axiomatic bargaining solution when coalitions employ threats that must be consistent with their solutions. As in Nash, our solution maximizes a (possibly weighted) product of payoffs for each coalition, but subcoalitional threats appear as conventional constraints that are not netted out when maximizing the Nash product. We study different aspects of this coalitional solution, including its connections to a notion of “pragmatic egalitarianism”. We then embed the solution into a setting with externalities, and define viable coalitional structures, under which every coalition follows its coalitional solution but interacts noncooperatively with other coalitions. We discuss applications to public goods, R&D coalitions, oligopoly cartels, and hospital networks.