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Evolutionary games on graphs and the speed of the evolutionary process. (English) Zbl 1202.91027
Authors’ abstract: 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.

##### MSC:
 91A22 Evolutionary games 91A43 Games involving graphs 05C57 Games on graphs (graph-theoretic aspects)
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