The authors propose a new approach concerning evolutionary equilibrium models, e.g. EES, introduced by \textit{J. Maynard Smith} [Evolution and the theory of games, Cambridge Univ. Press (1982; Zbl 0526.90102)]. By the model proposed one analyzes the situation in which a population of \(n\) players is randomly matched to play a normal form game \(G\). The payoffs of this game, from an economical point of view represent the fitness associated with the various outcomes. Unlike the standard EES framework, the \(n\) players here are rational decision-makers. They have preferences over outcomes and they form conjectures about the behavior of the other agents. Based on these they make choices which are optimal given their preferences. These preferences are represented by an evolutionary process. The authors finally show that when evolution selects individuals on the basis of the fitness of the actions they take, the aggregate distribution of action-profiles has to be a Nash equilibrium of \(G\).