Simulation of the weighted spatio-structured three cornered game and its satatistical properties

Abstract

In this article, we study the evolution of the strategies in a sort of weighted three cornered game, Glico Game. This game has three strategies in each agent and three parameters in the payoff matrix. We divide the parameter region into 8 areas and explore its qualitative and quantitative properties of the evolution of strategies which include Haming distance, correlation functions and the population sequence of each strategy. When the three payoff parameters take nearly values each other, the complex patterns mainly appear and as the difference of parameter values are enlarged, some peculiar strategy trends to be dominant gradually. An interesting fact is that the strongest strategy in the payoff do not necessarily dominate the latice world. There are even the cases where the weakest strategy in the payof dominate. Generally many cases have some period much shoter than the dimension of the configuration space.