We investigate an extension of Dekel, Ely and Yilankaya's (2004) treatment of the evolution of preference to more general, possibly nonexpected utility preferences. Along the lines of their analysis we consider a population of types that is repeatedly and randomly matched to play the mixed extension of any given symmetric two-player normalform game with complete information. In our setup, a type is a generic best-response correspondence that is assumed to satisfy only standard assumptions. Preferences evolve according to the "success" of the player which is determined by the payoff she receives in the game. As in Dekel, Ely and Yilankaya (2004), the players observe the type of their opponent and a Nash equilibrium according to their best responses is played. We show that Dekel, Ely and Yilankaya's result that stability of an outcome implies efficiency is robust in this more general setup. However, in our model we obtain full equivalence between the two concepts for 2x2 games. We show that efficiency of any strategy also implies the stability of the outcome that it induces. This is in contrast to the former work in which only efficiency of a pure strategy leads to a stable outcome. The result implies the existence of a stable outcome in any 2x2 game. Considering the class of rank-dependent expected utility preferences as example we discuss the model's ability to embed specific types of non-expected utility theories. Moreover, we study implications for well-established games like the prisoner's dilemma.
