Mutation-Selection Equilibrium in Games with Multiple Strategies

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Mutation-Selection Equilibrium in Games with Multiple Strategies

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Title: Mutation-Selection Equilibrium in Games with Multiple Strategies
Author: Antal, Tibor; Traulsen, Arne; Ohtsuki, Hisashi; Tarnita, Corina Elena; Nowak, Martin A.

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Citation: Antal, Tibor, Arne Traulsen, Hisashi Ohtsuki, Corina E. Tarnita, and Martin A. Nowak. 2009. Mutation–selection equilibrium in games with multiple strategies. Journal of Theoretical Biology 258(4): 614-622.
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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.
Published Version: doi:10.1016/j.jtbi.2009.02.010
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