Evolutionary Games on Star Graphs Under Various Updating Rules

It is known that in homogeneous populations the choice of the update rule is not critical in the evolutionary process. In this paper we investigate an evolutionary game between two strategies, A and B, interacting on a star graph considering four important update rules. We find explicit expressions for the fixation probability of any number of mutants placed at any position on the star, and the time to absorption (elimination or fixation of mutants) and fixation (absorption conditional on fixation occurring). For each of the update rules, we find appropriate conditions under which one strategy is favoured over the other. Considering the case where individuals have fixed fitness and a specific example of a Hawk-Dove game we then examine the effect of the update rule on the three quantities we study, and we show that in contrast with homogeneous populations, the choice of the update rule might be crucial for the evolutionary process in a non-homogeneous population.