From Rock Scissor Paper to study and modeling of Chinese Five Elements: Evolutionary Game Theory

Abstract

In this thesis, we have developed a model to study the behavior of an extended version of evolutionary game "Rock-Scissor-Paper", that is "Five Elements". The origin of five elements are from "Chinese five elements" in which five different types of elements compete with each other in a similar way as in a SIR model. Elements are affecting each other in two different ways, either to compete with each other or to help some particular elements in resisting their superior elements. The competition and cooperation is linked in circle which initiates a steady state. The analytical expressions (mean field) and simulation results have been presented. We have made some basic simulations of the original "Rock-Scissor-Paper" in order to build a better understanding of this kind of evolutionary game, and to extend from three elements to five elements. One of the real examples of five elements we have studied is a game called "Rock-Paper-Scissor-Lizard-Spock", which is a direct extension from the "Rock-Scissor-paper". Cooperation in the game is expressed in form of either direct cooperation/help from different elements as in "Chinese Five Elements" or indirect help caused by direct competition. Based on the simulations, some characteristic behaviors of five elements have been found. Reaction rates and different competition probabilities have proven to be the critical part in the game.