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Subgame perfect equilibria in majoritarian bargaining

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  • Herings, P. Jean-Jacques
  • Meshalkin, Andrey
  • Predtetchinski, Arkadi

Abstract

We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory experiments show various deviations from this equilibrium, where different offers are typically made and delay may occur before acceptance. We address the issue to what extent these findings are compatible with subgame perfect equilibrium and characterize the set of subgame perfect equilibrium payoffs for any value of the discount factor. We show that for any proposal in the interior of the space of possible agreements there exists a discount factor such that the proposal is made and accepted. We characterize the values of the discount factor for which equilibria with one-period delay exist. We show that any amount of equilibrium delay is possible and we construct subgame perfect equilibria such that arbitrary long delay occurs with probability one.

Suggested Citation

  • Herings, P. Jean-Jacques & Meshalkin, Andrey & Predtetchinski, Arkadi, 2018. "Subgame perfect equilibria in majoritarian bargaining," Journal of Mathematical Economics, Elsevier, vol. 76(C), pages 101-112.
    • Handle: RePEc:eee:mateco:v:76:y:2018:i:c:p:101-112
    DOI: 10.1016/j.jmateco.2018.03.007
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    Cited by:

    1. Andrzej Baranski & Caleb A. Cox, 2023. "Communication in multilateral bargaining with joint production," Experimental Economics, Springer;Economic Science Association, vol. 26(1), pages 55-77, March.
    2. repec:nad:wpaper:20220080 is not listed on IDEAS
    3. Bradfield, Anthony J. & Kagel, John H., 2015. "Legislative bargaining with teams," Games and Economic Behavior, Elsevier, vol. 93(C), pages 117-127.
    4. Beviá, Carmen & Corchón, Luis C. & Yasuda, Yosuke, 2024. "Folk theorem under bankruptcy," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    5. Duozhe Li, 2014. "Multiplicity of Equilibrium Payoffs in Three-Player Baron-Ferejohn Model," Economics Bulletin, AccessEcon, vol. 34(2), pages 1122-1132.
    6. Berry, Kevin & Delmond, Anthony R. & Morin Chassé, Rémi & Strandholm, John C. & Shogren, Jason F., 2022. "A bargaining experiment under weak property rights, with implications for indigenous title claims," Ecological Economics, Elsevier, vol. 198(C).
    7. Andrzej Baranski & Caleb A. Cox, 2019. "Communication in Multilateral Bargaining with Joint Production," Working Papers 20190032, New York University Abu Dhabi, Department of Social Science, revised Nov 2019.
    8. Baranski, Andrzej & Haas, Nicholas, 2023. "The timing of communication and retaliation in bargaining: An experimental study," Journal of Economic Psychology, Elsevier, vol. 96(C).

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    More about this item

    Keywords

    Dynamic games; Bargaining; Majoritarian voting; Subgame perfect equilibrium; Delay of acceptance;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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