Credibilistic Bimatrix Games with Loss Aversion and Triangular Fuzzy Payoffs

Abstract

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.