Bimatrix games are reconsidered under assumption that players are loss averse and payoffs are fuzzy, where reference points are given exogenously. The impact of loss aversion on bimatrix game is investigated by applying credibility theory. Three solution concepts of credibilistic loss aversion Nash equilibria (i.e., expected loss aversion Nash equilibrium, optimistic loss aversion Nash equilibrium and pessimistic loss aversion Nash equilibrium) and their existence theorems are proposed. The sufficient and necessary conditions are presented to find three equilibria. It is found that three credibilistic loss aversion Nash equilibria are equivalent if confidence level is equal to 0.5. Furthermore, an analysis on credibilistic loss aversion equilibria with respect to loss aversion is performed in a 2 × 2 bimatrix game with triangular fuzzy payoffs. It is found that with a higher probability a more loss-averse player receives a preferred payoff in the mixed strategy Nash equilibrium in some situations, but receives the second highest payoff in other situations. Finally, a case study is shown to illustrate the validity of the bimatrix game with triangular fuzzy payoffs developed in this paper.

中文翻译：

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具有损失回避和三角模糊收益的Creditbilistic Bimatrix游戏

在假定玩家避免损失并且收益是模糊的假设下重新考虑Bimatrix游戏，其中参考点是外生的。应用可信度理论研究了损失厌恶对双子博弈的影响。提出了信用损失厌恶纳什均衡的三种解决方案（即预期损失厌恶纳什均衡，乐观损失厌恶纳什均衡和悲观损失厌恶纳什均衡）及其存在定理。提出了找到三个平衡点的充分必要条件。如果置信水平等于0.5，则发现三个信用损失厌恶纳什均衡是等效的。此外，在具有三角形模糊收益的2×2双矩阵博弈中，对损失厌恶相关的发信性损失厌恶均衡进行了分析。发现在某些情况下，厌恶厌恶的玩家更有可能在混合策略纳什均衡中获得偏好的回报，而在其他情况下则获得第二高的回报。最后，通过一个案例研究来说明本文开发的具有三角模糊收益的双矩阵博弈的有效性。