Classical, Modern, and New Garne Theory

This paper is a brief history of game theory with its main theme being the nature of the decision makers assumed in the various stages of its historical development. It demonstrates that changes in the "image of man" nourished the developments of what many believe to be progress in game theory. The first stage, classical game theory, is defined by John von Neumann's and Oskar Morgenstern's pioneering book "Game Theory and Economic Behaviour" which introduced the concept of individual rational players and focuses on conflicting interests. The second stage, modern game theory, is defined by the Nash player who is not only rational but, at least implicitly, assumes that all players are rational to such a degree that players can coordinate their strategies so that a Nash equilibrium prevails. The third stage, new game theory, is defined by the Harsanyi player who is rational but knows very little about the other players, e.g., their payoff functions or the way they form beliefs about other players' payoff functions or beliefs. The Harsanyi player either plays a highly sophisticated epistemic game on the forming of beliefs or rests content with himself by imitating the observed successful behavior of other agents.