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Bargaining with endogenous disagreement: The extended Kalai–Smorodinsky solution

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  • Bozbay, Irem
  • Dietrich, Franz
  • Peters, Hans

Abstract

Following Vartiainen (2007) we consider bargaining problems in which no exogenous disagreement outcome is given. A bargaining solution assigns a pair of outcomes to such a problem, namely a compromise outcome and a disagreement outcome: the disagreement outcome may serve as a reference point for the compromise outcome, but other interpretations are given as well. For this framework we propose and study an extension of the classical Kalai–Smorodinsky bargaining solution. We identify the (large) domain on which this solution is single-valued, and present two axiomatic characterizations on subsets of this domain.

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  • Bozbay, Irem & Dietrich, Franz & Peters, Hans, 2012. "Bargaining with endogenous disagreement: The extended Kalai–Smorodinsky solution," Games and Economic Behavior, Elsevier, vol. 74(1), pages 407-417.
    • Handle: RePEc:eee:gamebe:v:74:y:2012:i:1:p:407-417
    DOI: 10.1016/j.geb.2011.06.007
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    1. Carmen Herrero, 1997. "Endogenous reference points and the adjusted proportional solution for bargaining problems with claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 113-119.
    2. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    3. Vartiainen, Hannu, 2007. "Collective choice with endogenous reference outcome," Games and Economic Behavior, Elsevier, vol. 58(1), pages 172-180, January.
    4. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    5. Thomson, William, 1981. "A class of solutions to bargaining problems," Journal of Economic Theory, Elsevier, vol. 25(3), pages 431-441, December.
    6. Peters, H.J.M. & Tijs, S.H., 1985. "Characterization of all individually monotonic bargaining solutions," Other publications TiSEM 52f5a6d5-dcac-4fec-9b8e-9, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Khan, Abhimanyu, 2022. "Expected utility versus cumulative prospect theory in an evolutionary model of bargaining," Journal of Economic Dynamics and Control, Elsevier, vol. 137(C).
    2. 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.
    3. Rudy Henkel, 2021. "Multiself Bargaining," Studies in Microeconomics, , vol. 9(1), pages 28-65, June.
    4. Llorente-Saguer, Aniol & Zultan, Ro’i, 2017. "Collusion and information revelation in auctions," European Economic Review, Elsevier, vol. 95(C), pages 84-102.
    5. Emin Karagözoğlu & Kerim Keskin, 2018. "Endogenous reference points in bargaining," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(2), pages 283-295, October.

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    More about this item

    Keywords

    C78; D74; Axiomatic bargaining; Endogenous disagreement outcome; Extended Kalai–Smorodinsky solution;
    All these keywords.

    JEL classification:

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

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