×

zbMATH — the first resource for mathematics

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)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Antal, Bulletin of mathematical biology 68 (8) pp 1923– (2006) · Zbl 1296.92238 · doi:10.1007/s11538-006-9061-4
[2] Broom, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464 (2098) pp 2609– (2008) · Zbl 1152.92341 · doi:10.1098/rspa.2008.0058
[3] J INTERDISCIPL MATH 12 pp 129– (2009) · Zbl 1177.92024 · doi:10.1080/09720502.2009.10700618
[4] Hauert, Nature; Physical Science (London) 428 (6983) pp 643– (2004) · doi:10.1038/nature02360
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.