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Journal Article

Mutation-selection equilibrium in games with multiple strategies

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons56973

Traulsen,  Arne
Department Evolutionary Ecology, Max Planck Institute for Evolutionary Biology, Max Planck Society;
Research Group Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Max Planck Society;

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Citation

Antal, T., Traulsen, A., Ohtsuki, H., Tarnita, C. E., & Nowak, M. A. (2009). Mutation-selection equilibrium in games with multiple strategies. Journal of Theoretical Biology, 258(4), 614-622. doi:10.1016/j.jtbi.2009.02.010.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-D5A1-E
Abstract
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright–Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of n×n games in the limit of weak selection.