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The Probability to Reach an Agreement as a Foundation for Axiomatic Bargaining

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  • Lorenzo Bastianello
  • Marco LiCalzi

Abstract

We revisit the Nash bargaining model and axiomatize a procedural solution that maximizes the probability of successful bargaining. Our characterization spans several known solution concepts, including the special cases of the Nash, egalitarian, and utilitarian solutions. Using a probability‐based language, we offer a natural interpretation for the product operator underlying the Nash solution: when the bargainers' individual acceptance probabilities are independent, their product recovers the joint acceptance probability.

Suggested Citation

  • Lorenzo Bastianello & Marco LiCalzi, 2019. "The Probability to Reach an Agreement as a Foundation for Axiomatic Bargaining," Econometrica, Econometric Society, vol. 87(3), pages 837-865, May.
    • Handle: RePEc:wly:emetrp:v:87:y:2019:i:3:p:837-865
    DOI: 10.3982/ECTA13673
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    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    3. Marco LiCalzi, 2005. "A language for the construction of preferences under uncertainty," Game Theory and Information 0509002, University Library of Munich, Germany.
    4. Erio Castagnoli & Marco LiCalzi, 2005. "Expected utility without utility," Game Theory and Information 0508004, University Library of Munich, Germany.
    5. Rubinstein, Ariel & Safra, Zvi & Thomson, William, 1992. "On the Interpretation of the Nash Bargaining Solution and Its Extension to Non-expected Utility Preferences," Econometrica, Econometric Society, vol. 60(5), pages 1171-1186, September.
    6. Trockel, W., 2008. "The Nash product is a utility representation of the Pareto ordering," Economics Letters, Elsevier, vol. 99(2), pages 220-222, May.
    7. John C. Harsanyi & Reinhard Selten, 1972. "A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information," Management Science, INFORMS, vol. 18(5-Part-2), pages 80-106, January.
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    Cited by:

    1. Harstad, Bård, 2023. "Pledge-and-review bargaining," Journal of Economic Theory, Elsevier, vol. 207(C).
    2. Harstad, Bård, 2021. "A Theory of Pledge-and-Review Bargaining," Memorandum 5/2022, Oslo University, Department of Economics, revised 21 Jun 2021.
    3. Luis C. Dias & Rudolf Vetschera, 2022. "Two-party Bargaining Processes Based on Subjective Expectations: A Model and a Simulation Study," Group Decision and Negotiation, Springer, vol. 31(4), pages 843-869, August.
    4. William Thomson, 2022. "On the axiomatic theory of bargaining: a survey of recent results," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 491-542, December.
    5. Yoshio Kamijo, 2023. "Fixation of inequality and emergence of the equal split norm: Approach from behavioral bargaining theory," Working Papers 2209, Waseda University, Faculty of Political Science and Economics, revised Jun 2023.

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    More about this item

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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