A STOCHASTIC BEHAVIORAL-MODEL AND A MICROSCOPIC FOUNDATION OF EVOLUTIONARY GAME-THEORY

A stochastic model is developed to describe behavioral changes by imit ative pair interactions of individuals. 'Microscopic' assumptions on t he specific form of the imitative processes lead to a stochastic versi on of the game dynamical equations, which means that the approximate m ean value equations of these equations are the game dynamical equation s of evolutionary game theory. The stochastic version of the game dyna mical equations allows the derivation of covariance equations. These s hould always be solved along with the ordinary game dynamical equation s. On the one hand, the average behavior is affected by the covariance s so that the game dynamical equations must be corrected for increasin g covariances; otherwise they may become invalid in the course of time . On the other hand, the covariances are a measure of the reliability of game dynamical descriptions. An increase of the covariances beyond a critical value indicates a phase transition, i.e. a sudden change in the properties of the social system under consideration. The applicab ility and use of the equations introduced are illustrated by computati onal results for the social self-organization of behavioral convention s.