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International Journal of Fuzzy Systems

, Volume 21, Issue 3, pp 892–907 | Cite as

Loss Aversion Equilibrium of Bimatrix Games with Symmetric Triangular Fuzzy Payoffs

  • Chunsheng Cui
  • Zhongwei Feng
  • Chunqiao TanEmail author
  • Surajit Borkotokey
Article

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.

Keywords

Bimatrix game Symmetric triangular fuzzy payoffs Loss aversion Fuzzy set theory (α, β)-loss aversion Nash equilibrium 

Notes

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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Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  • Chunsheng Cui
    • 1
  • Zhongwei Feng
    • 2
  • Chunqiao Tan
    • 2
    • 3
    Email author
  • Surajit Borkotokey
    • 4
  1. 1.School of InformationBeijing Wuzi UniversityBeijingChina
  2. 2.School of BusinessCentral South UniversityChangshaChina
  3. 3.School of Government AuditNanjing Audit UniversityNanjingChina
  4. 4.Department of MathematicsDibrugarh UniversityDibrugarhIndia

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