On Loss Aversion in Bimatrix Games

In this paper we study three different types of loss aversion equi- libria in bimatrix games. Loss aversion equilibria are Nash equilibria of games where players are loss averse and where the reference points – points below which they consider payoffs to be losses – are endoge- nous to the equilibrium calculation. The first type is the fixed point loss aversion equilibrium, introduced in Shalev (2000) under the name of ‘myopic loss aversion equilibrium’. There, the players’ reference points depend on the beliefs about their opponents’ strategies. The second type, the maximin loss aversion equilibrium, differs from the fixed point loss aversion equilibrium in that the reference point is now only based on the carrier of the players’ beliefs, not on the exact prob- abilities. In the third, the safety level loss aversion equilibrium, this dependence is completely dispensed with. Finally, we do a compara- tive statics analysis of all three equilibrium concepts in 2 × 2 bimatrix games. The results indicate that a player, under some conditions, benefits from his opponent falsely believing he is loss averse.