Restricted non-cooperative games

Abstract

Traditional non-cooperative game theory has been an extraordinarily powerful tool in modeling biological and economic behavior, as well as the effect of legal rules. And, although it contains plausible concepts of equilibrium behavior, it does not contain a theory of dynamics as to how equilibria are to be reached. This paper on Restricted Non-Cooperative Games inserts dynamic content into traditional game theory and thus permits modeling of more realistic settings by imposing topologies that restrict the strategies available to players. It uses Mathematica to show how the payoff array used in conventional game theory, coupled with these strategy topologies, can construct a "game network", which can be further visualized, analyzed, and "scored" for each of the players. The paper likewise uses Mathematica to analyze settings in which each player has the ability to engineer its own strategy topology and suggests other potential extensions of Restricted Non-Cooperative Games.1 © Springer-Verlag Berlin Heidelberg 2007.