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On Loss Aversion in Bimatrix Games

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  • Bram Driesen

    ()

  • Andrés Perea

    ()

  • Hans Peters

    ()

Abstract

In this paper we study three different types of loss aversion equilibria in bimatrix games. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points – points below which they consider payoffs to be losses – are endogenous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000) under the name of ‘myopic loss aversion equilibrium’. There, the players’ reference points depend on the beliefs about their opponents’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference point is now only based on the carrier of the players’ beliefs, not on the exact probabilities. In the third, the safety level loss aversion equilibrium, this dependence is completely dispensed with. Finally, we do a comparative statics analysis of all three equilibrium concepts in 2-by-2 bimatrix games. The results indicate that a player, under some conditions, benefits from his opponent falsely believing he is loss averse.

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Bibliographic Info

Article provided by Springer in its journal Theory and Decision.

Volume (Year): 68 (2010)
Issue (Month): 4 (April)
Pages: 367-391

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Handle: RePEc:kap:theord:v:68:y:2010:i:4:p:367-391

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Web page: http://www.springerlink.com/link.asp?id=100341

Related research

Keywords: bimatrix games; loss aversion; reference-dependence; C72;

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  1. Jonathan Shalev, 2000. "Loss aversion equilibrium," International Journal of Game Theory, Springer, vol. 29(2), pages 269-287.
  2. Schoemaker, Paul J H, 1982. "The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations," Journal of Economic Literature, American Economic Association, vol. 20(2), pages 529-63, June.
  3. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
  4. Fershtman, Chaim, 1996. "On the value of incumbency managerial reference points and loss aversion," Journal of Economic Psychology, Elsevier, vol. 17(2), pages 245-257, April.
  5. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  6. Bram Driesen & Andrés Perea & Hans Peters, 2010. "On Loss Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 68(4), pages 367-391, April.
  7. Camerer, Colin F., 1998. "Prospect Theory in the Wild: Evidence From the Field," Working Papers 1037, California Institute of Technology, Division of the Humanities and Social Sciences.
  8. Caroline Berden & Hans Peters, 2006. "On the Effect of Risk Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 60(4), pages 359-370, 06.
  9. Dekel, Eddie & Safra, Zvi & Segal, Uzi, 1991. "Existence and dynamic consistency of Nash equilibrium with non-expected utility preferences," Journal of Economic Theory, Elsevier, vol. 55(2), pages 229-246, December.
  10. John C. Hershey & Howard C. Kunreuther & Paul J. H. Schoemaker, 1982. "Sources of Bias in Assessment Procedures for Utility Functions," Management Science, INFORMS, vol. 28(8), pages 936-954, August.
  11. Machina, Mark J, 1987. "Choice under Uncertainty: Problems Solved and Unsolved," Journal of Economic Perspectives, American Economic Association, vol. 1(1), pages 121-54, Summer.
  12. Crawford, Vincent P., 1990. "Equilibrium without independence," Journal of Economic Theory, Elsevier, vol. 50(1), pages 127-154, February.
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Cited by:
  1. Peters, Hans, 2012. "A preference foundation for constant loss aversion," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 21-25.
  2. Bram Driesen & Andrés Perea & Hans Peters, 2010. "On Loss Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 68(4), pages 367-391, April.

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