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Bargaining under liquidity constraints: Unified strategic foundations of the Nash and Kalai solutions

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  • Hu, Tai-Wei
  • Rocheteau, Guillaume

Abstract

We provide unified strategic foundations for the Nash (1950) and Kalai (1977) solutions in the context of negotiations under liquidity constraints. We propose an N-round game where in each round a seller and a buyer with limited payment capacity negotiate a bundle of divisible goods, where bundle sizes can vary across rounds, according to Rubinstein's (1982) alternating-offer game. The game implements the Nash solution if N=1 and the Kalai solution if N=+∞ and bundle sizes are infinitesimal. If N is set by one player ex ante, the buyer chooses N=1 while the seller chooses N=+∞. We endogenize liquidity constraints and show they bind for all N<+∞, even when there is no cost in holding liquidity.

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  • Hu, Tai-Wei & Rocheteau, Guillaume, 2020. "Bargaining under liquidity constraints: Unified strategic foundations of the Nash and Kalai solutions," Journal of Economic Theory, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:jetheo:v:189:y:2020:i:c:s0022053120300910
    DOI: 10.1016/j.jet.2020.105098
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    Cited by:

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    2. Amendola, Nicola & Araujo, Luis & Ferraris, Leo, 0. "Physical vs digital currency: a difference that makes a difference," Theoretical Economics, Econometric Society.
    3. Duffy, John & Lebeau, Lucie & Puzzello, Daniela, 2025. "Bargaining under liquidity constraints: Experimental evidence," Journal of Economic Theory, Elsevier, vol. 228(C).
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    6. Nicola Amendola & Luis Araujo & Leo Ferraris, 2024. "Physical vs Digital Currency: What's the Difference, Why it Matters," Working Papers 537, University of Milano-Bicocca, Department of Economics.
    7. Caparrós, By Alejandro & Pereau, Jean-Christophe, 2021. "Inefficient coasean negotiations over emissions and transfers," Journal of Economic Behavior & Organization, Elsevier, vol. 189(C), pages 359-378.
    8. Roberto Serrano, 2021. "Sixty-seven years of the Nash program: time for retirement?," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 35-48, March.
    9. Choi, Michael & Rocheteau, Guillaume, 2024. "Foundations of market power in monetary economies," Journal of Economic Theory, Elsevier, vol. 222(C).
    10. John Duffy & Lucie Lebeau & Daniela Puzzello, 2021. "Bargaining Under Liquidity Constraints: Nash vs. Kalai in the Laboratory," Working Papers 2113, Federal Reserve Bank of Dallas.
    11. Chatterjee, Kalyan & Chaturvedi, Rakesh, 2024. "Integrating Raiffa and Nash approaches to bargaining using interim agreements," Games and Economic Behavior, Elsevier, vol. 146(C), pages 105-120.
    12. Hu, Tai-Wei & Li, Yiting & Liu, Yilei, 2025. "Optimal banking regulation and monetary policy," European Economic Review, Elsevier, vol. 178(C).
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    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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