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The Kalai-Smorodinsky bargaining solution with loss aversion

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  • Driesen, Bram
  • Perea, Andrés
  • Peters, Hans

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.

Suggested Citation

  • Driesen, Bram & Perea, Andrés & Peters, Hans, 2011. "The Kalai-Smorodinsky bargaining solution with loss aversion," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 58-64, January.
  • Handle: RePEc:eee:matsoc:v:61:y:2011:i:1:p:58-64
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    References listed on IDEAS

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    1. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 121(4), pages 1133-1165.
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    5. Jonathan Shalev, 2002. "Loss Aversion and Bargaining," Theory and Decision, Springer, vol. 52(3), pages 201-232, May.
    6. Hans Peters & Eric Van Damme, 1991. "Characterizing the Nash and Raiffa Bargaining Solutions by Disagreement Point Axioms," Mathematics of Operations Research, INFORMS, vol. 16(3), pages 447-461, August.
    7. Peters, Hans, 2012. "A preference foundation for constant loss aversion," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 21-25.
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    9. Jonathan Shalev, 2000. "Loss aversion equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(2), pages 269-287.
    10. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
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    Cited by:

    1. Driesen, Bram, 2012. "Proportional concessions and the leximin solution," Economics Letters, Elsevier, vol. 114(3), pages 288-291.
    2. Schumacher, Heiner & Karle, Heiko & Volund, Rune, 2016. "Settlement Offers," Annual Conference 2016 (Augsburg): Demographic Change 145772, Verein für Socialpolitik / German Economic Association.

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