City Research Online

Evolutionary games on graphs and the speed of the evolutionary process

Broom, M., Hadjichrysanthou, C. and Rychtar, J. (2010). Evolutionary games on graphs and the speed of the evolutionary process. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 466(2117), pp. 1327-1346. doi: 10.1098/rspa.2009.0487

Abstract

In this paper, we investigate evolutionary games with the invasion process updating rules on three simple non-directed graphs: the star, the circle and the complete graph. Here, we present an analytical approach and derive the exact solutions of the stochastic evolutionary game dynamics. We present formulae for the fixation probability and also for the speed of the evolutionary process, namely for the mean time to absorption (either mutant fixation or extinction) and then the mean time to mutant fixation. Through numerical examples, we compare the different impact of the population size and the fitness of each type of individual on the above quantities on the three different structures. We do this comparison in two specific cases. Firstly, we consider the case where mutants have fixed fitness r and resident individuals have fitness 1. Then, we consider the case where the fitness is not constant but depends on games played among the individuals, and we introduce a ‘hawk–dove’ game as an example.

Publication Type: Article
Publisher Keywords: evolutionary dynamics, star graph, structured population, game theory, fixation probability, fixation time
Subjects: H Social Sciences > HA Statistics
Q Science > QH Natural history
Departments: School of Mathematics, Computer Science & Engineering > Mathematics
URI: http://openaccess.city.ac.uk/id/eprint/1005
[img]
Preview
PDF
Download (543kB) | Preview

Export

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login