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The Kalai-Smorodinsky solution with loss aversion

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  • Driesen, B.W.I.

    (Quantitative Economics)

  • Perea ý Monsuwé, A.

    (Quantitative Economics)

  • Peters, H.J.M.

    (Quantitative Economics)

Abstract

We consider bargaining problems under the assumption that players are loss averse, i.e., experience disutility from obtaining an outcome lower than some reference point. We follow the approach of Shalev (2002) by imposing the self-supporting condition on an outcome: an outcome z in a bargaining problem is self-supporting under a given bargaining solution, whenever transforming the problem using outcome z as a reference point, yields a transformed problem in which the solution is z. We show that n-player bargaining problems have a unique self-supporting outcome under the Kalai-Smorodinsky solution. For all possible loss aversion coefficients we determine the bargaining solutions that give exactly these outcomes, and characterize them by the standard axioms of Scale Invariance, Individual Monotonicity, and Strong Individual Rationality, and a new axiom called Proportional Concession Invariance (PCI). A bargaining solution satisfies PCI if moving the utopia point in the direction of the solution outcome does not change this outcome.
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Suggested Citation

  • Driesen, B.W.I. & Perea ý Monsuwé, A. & Peters, H.J.M., 2009. "The Kalai-Smorodinsky solution with loss aversion," Research Memorandum 030, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  • Handle: RePEc:unm:umamet:2009030
    DOI: 10.26481/umamet.2009030
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    1. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1133-1165.
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    Cited by:

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    3. Wentao Yi & Zhongwei Feng & Chunqiao Tan & Yuzhong Yang, 2021. "Green Supply Chain Management with Nash Bargaining Loss-Averse Reference Dependence," Mathematics, MDPI, vol. 9(24), pages 1-26, December.
    4. Qi Feng & Yuanchen Li & J. George Shanthikumar, 2022. "Negotiations in Competing Supply Chains: The Kalai-Smorodinsky Bargaining Solution," Management Science, INFORMS, vol. 68(8), pages 5868-5890, August.
    5. Chunsheng Cui & Zhongwei Feng & Chunqiao Tan, 2018. "Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    6. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
    7. 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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