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The Kalai-Smorodinsky bargaining solution with loss aversion

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

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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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 61 (2011)
Issue (Month): 1 (January)
Pages: 58-64

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Handle: RePEc:eee:matsoc:v:61:y:2011:i:1:p:58-64
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  1. Peters, H.J.M. & Tijs, S.H., 1984. "Individually monotonic bargaining solutions of n-person bargaining games," Other publications TiSEM 94ffcb19-a0bc-4364-a42e-7, Tilburg University, School of Economics and Management.
  2. Kobberling, Veronika & Peters, Hans, 2003. "The effect of decision weights in bargaining problems," Journal of Economic Theory, Elsevier, vol. 110(1), pages 154-175, May.
  3. Botond Koszegi & Matthew Rabin, 2004. "A Model of Reference-Dependent Preferences," Method and Hist of Econ Thought 0407001, EconWPA.
  4. Sugden, Robert, 2003. "Reference-dependent subjective expected utility," Journal of Economic Theory, Elsevier, vol. 111(2), pages 172-191, August.
  5. Peters Hans, 2010. "A preference foundation for constant loss aversion," Research Memorandum 062, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  6. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
  7. Jonathan Shalev, 2000. "Loss aversion equilibrium," International Journal of Game Theory, Springer, vol. 29(2), pages 269-287.
  8. Jonathan Shalev, 1996. "Loss Aversion and Bargaining," Game Theory and Information 9606001, EconWPA, revised 18 Mar 1997.
  9. Kannai, Yakar, 1977. "Concavifiability and constructions of concave utility functions," Journal of Mathematical Economics, Elsevier, vol. 4(1), pages 1-56, March.
  10. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
  11. van Damme, E.E.C. & Peters, H., 1991. "Characterizing the Nash and Raiffa bargaining solutions by disagreement point axioms," Other publications TiSEM 4bd5eb9e-328a-45a0-aa0a-e, Tilburg University, School of Economics and Management.
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