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Loss Aversion Equilibrium of Bimatrix Games with Symmetric Triangular Fuzzy Payoffs

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Abstract

Inspired by Shalev’s model of loss aversion, we propose a bimatrix game with loss aversion, where the elements in payoff matrices are characterized as symmetric triangular fuzzy numbers, and investigate the effect of loss aversion on equilibrium strategies. Firstly, we define a solution concept of (α, β)-loss aversion Nash equilibrium and prove that it exists in any bimatrix game with loss aversion and symmetric triangular fuzzy payoffs. Furthermore, a sufficient and necessary condition is proposed to find the (α, β)-loss aversion Nash equilibrium. Finally, for a 2 × 2 bimatrix game with symmetric triangular fuzzy payoffs, the relation between the (α, β)-loss aversion Nash equilibrium and loss aversion coefficients is discussed when players are loss averse and it is analyzed when a player can benefit from his opponent’s misperceiving belief about his loss aversion level.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Nos. 71671188 and 71874112), Beijing Intelligent Logistics System Collaborative Innovation Center (BILSCIC-2018KF-04), and Natural Science Foundation of Hunan Province, China (2016JJ1024).

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Authors and Affiliations

  1. School of Information, Beijing Wuzi University, Beijing, 101149, China

    Chunsheng Cui

  2. School of Business, Central South University, Changsha, 410083, China

    Zhongwei Feng & Chunqiao Tan

  3. School of Government Audit, Nanjing Audit University, Nanjing, 211815, China

    Chunqiao Tan

  4. Department of Mathematics, Dibrugarh University, Dibrugarh, Assam, 786004, India

    Surajit Borkotokey

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  1. Chunsheng Cui
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  2. Zhongwei Feng
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Correspondence to Chunqiao Tan.

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Cui, C., Feng, Z., Tan, C. et al. Loss Aversion Equilibrium of Bimatrix Games with Symmetric Triangular Fuzzy Payoffs. Int. J. Fuzzy Syst. 21, 892–907 (2019). https://doi.org/10.1007/s40815-019-00611-3

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  • DOI: https://doi.org/10.1007/s40815-019-00611-3

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