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 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 player. It uses Mathematica to show how the payoff array used in conventional game theory can operate to generate a game network from the players' strategy topologies. Mathematica is likewise used to visualize this process and analyze the resulting game networks for properties such as maximal cycle lengths, stationary probabilities of associated Markov transition matrices, and scores for each of the players. The framework further analyzes settings in which each player has the ability to engineer its own strategy topology and suggests other potential extensions of Restricted Non-Cooperative Games.