Prospect Theory and mixed-strategy Nash Equilibria in 2x2 Games

The problem of finding mixed-strategy Nash Equilibria in 2x2 Games, has been widely explored using the classical Expected Utility maximization criterion. In this paper we study the effects of using Prospect Theory in such a simple situations, involving only two possible strategies for each gambler. The results show how there is no variation in the sets of equilibrium points in all the trivial situations (i.e. when both gamblers have a dominant strategy). On the converse, when the gamblers play strategically, the probability distortion implied by Prospect Theory leads to the disappearance of some notable Nash Equilibria given to linearity in probability.