Loss Aversion Equilibrium of Bimatrix Games with Symmetric Triangular Fuzzy Payoffs

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.