Natural Selection between Two Games and Replicator Dynamics on Graphs

Abstract

In this paper I study the natural selection between two games to determine, which game will dominate in the community as a result of natural selection. The formalization of this question in the form of a parametrized game and the mathematical toolbox to solve it were recently developed in (Karev 2024). Here, I applied the developed approach to natural selection between games on graphs. Specifically, I compare standard games on a complete graph with games that have updated rules suggested by Ohtsuki and Nowak (2006). The results of the natural selection between the initial and updated games, or between different updated games were visualized through the evolution of the parameter distribution in corresponding parametrized game. The developed approach can be used for other problems, such as local replicator dynamics, pairwise competition, the game of alleles in diploid genomes (see Karev 2004) and cancer modeling (Kareva, Karev 2019).