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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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Suggested Citation

  • Bram Driesen & Andrés Perea & Hans Peters, 2010. "On Loss Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 68(4), pages 367-391, April.
    • Handle: RePEc:kap:theord:v:68:y:2010:i:4:p:367-391
    DOI: 10.1007/s11238-008-9102-6
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    1. Caroline Berden & Hans Peters, 2006. "On the Effect of Risk Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 60(4), pages 359-370, June.
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    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. 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.
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    1. Bram Driesen & Andrés Perea & Hans Peters, 2010. "On Loss Aversion in Bimatrix Games," Theory and Decision, Springer, vol. 68(4), pages 367-391, April.
    2. Dato, Simon & Grunewald, Andreas & Müller, Daniel & Strack, Philipp, 2017. "Expectation-based loss aversion and strategic interaction," Games and Economic Behavior, Elsevier, vol. 104(C), pages 681-705.
    3. 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.
    4. 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.
    5. Peters, Hans, 2012. "A preference foundation for constant loss aversion," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 21-25.
    6. Li, Qianwen & Qian, Tingyu & Zhang, Xufeng & Long, Ruyin & Chen, Hong & Huang, Han & Liu, Lei & Zhu, Licai & Jiang, Huikang & Zhu, Hanyi, 2023. "How does stakeholder loss aversion affect the promotion of green housing?," Economic Analysis and Policy, Elsevier, vol. 80(C), pages 647-668.

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    More about this item

    Keywords

    bimatrix games; loss aversion; reference-dependence; C72;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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