We model, using evolutionary game theory, the implications of endogenous determination of preferences over the outcomes of any given two-player normal form game, G. We consider a large population randomly and repeatedly matched to play G. Each individual has a preference relation over the outcomes of G which may be different than the "true" payoff function in G, and makes optimal choices given her preferences. The evolution of preferences is driven by the payoffs in G that each player obtains. We define stable outcomes (of G) as arising from the stable points of the evolutionary process described above. In our most general model players know the distribution of preferences in the population and observe their opponents' preferences with probability p. They then play a (Bayesian) Nash equilibrium of the resulting game of incomplete information. In the case in which players can perfectly observe their opponents' preferences, i.e., p=1, (where the game is actually one of complete information) an outcome is stable only if it is efficient. Also, an efficient outcome which arises from a strict Nash equilibrium is stable. We also characterize, for 2×2 games, both the stable outcomes and the stable distributions of preferences in the population. When preferences are unobservable, i.e., p=0, we show that stability in our model of evolution of preferences coincides with the notion of neutrally stable strategy (NSS). Finally, we consider robustness of these results. The necessity and sufficiency results are robust to slight changes in p, except for the sufficiency of NSS when p=0: There are in fact (Pareto-inferior) risk-dominant strict equilibria that are not stable for any p>0.
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