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Nash solutions for bargaining problems with a reference point

Author

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  • Olivier L’haridon

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Noemí Navarro

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique, UR - Université de Rennes)

Abstract

We explore the implications of the presence of a reference point on bargaining outcomes. We consider Nash's four original axioms with two additional axioms making use of the reference point: equal direction of changes and invariance with respect to the Shalev transformation (Shalev invariance). Because any solution that satisfies Pareto efficiency, scale invariance, contraction independence, and the two new axioms must be independent of the disagreement point when the reference point is feasible, we propose two notions of symmetry and derive two different solutions: the constrained Nash bargaining solution and the r-Nash bargaining solution. In addition to our main results, we include an axiomatic characterization of the disagreement solution.

Suggested Citation

  • Olivier L’haridon & Noemí Navarro, 2025. "Nash solutions for bargaining problems with a reference point," Post-Print hal-05326021, HAL.
    • Handle: RePEc:hal:journl:hal-05326021
    DOI: 10.1016/j.jebo.2025.107266
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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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