Microscopic foundation of stochastic game dynamical equations

Dirk Helbing

pp. 211-224

in: Werner Leinfellner, Eckehart Köhler (eds), Game theory, experience, rationality, Berlin, Springer, 1998

Abstract

Since von Neumann and Morgenstern initiated the field of game theory,¹ it has often proved of great value for the quantitative description and understanding of competition and co-operation between individuals. Game theory focusses on two questions: 1. Which is the optimal strategy in a given situation? 2. What is the dynamics of strategy choices in cases of repeatedly interacting individuals? In this connection game dynamical equations² find a steadily increasing interest. Although they agree with the replicator equations of evolution theory (cf. Sec. II), they cannot be justified in the same way. Therefore, we will be looking for a foundation of the game dynamical equations which is based on individual actions and decisions (cf. Sec. IV).