A review of evolutionary graph theory with applications to game theory.
Evolutionary graph theory (EGT), studies the ability of a mutant gene to overtake a finite structured population. In this review, we describe the original framework for EGT and the major work that has followed it. This review looks at the calculation of the "fixation probability" - the probability of a mutant taking over a population and focuses on game-theoretic applications. We look at varying topics such as alternate evolutionary dynamics, time to fixation, special topological cases, and game theoretic results. Throughout the review, we examine several interesting open problems that warrant further research.
Network Science Center and Dept. of Electrical Engineering and Computer Science, United States Military Academy, West Point, NY 10996, United States. paulo@shakarian.net
Paulo
P
Shakarian
Patrick
P
Roos
Anthony
A
Johnson
D005075:Biological Evolution; D005716:Game Theory; D040961:Genetic Drift; D008957:Models, Genetic; D009154:Mutation; D011157:Population Dynamics; D013997:Time Factors