Nash Bargaining in Coalitional Games

Rajiv Vohra and Debraj Ray
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Rajiv Vohra: Brown University
Debraj Ray: University of Warwick

The Warwick Economics Research Paper Series (TWERPS) from University of Warwick, Department of Economics

Abstract: 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.

Keywords: Nash bargaining; coalitional threats; strategic externalities JEL codes: C70; D60; D63 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:wrk:warwec:1633

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