The Evolution of Cellar Automaton based on Dilemmma Games with Selfish Strategy

Abstract

We have proposed two new evolutionary rules on spatio-iterated games that is not mimic evolution of strategies, and mainly discussed the Prisoner's Dilemma game \cite{toyota2} by the two evoutionary rules \cite{toyota3}. In this paper we focus the first rule, that is, the selfish evolutionary rule for various dilemma games. In contrast to the Prisoner's Dilemma, there are gererally rich pase structures in the dilemma games. First we analytically clear the structure to present phase diagrams in the various dilemma games. Forthermore we simulate the time evolution of the soatio-games in the some representatives of the parameters according to the phase diagrams. Including some mutations, detail investigations are made by a computer simulation for five kinds of initial configurations. As results we find some dualities and game invariant properties. They show a sort of bifurcation as a mutation parameter are varied. In the path from one period to two one some common features are observed in most of games and some chaotic behaviors appear in the middle of the transition. Lastly we estimate the total hamiltonian, which is defined by the sum of the total payoff of all agents in the system, and show that the chaotic period is best from the perspective of the payoff. We also made some primitive discussions on them.