Mutation-selection equilibrium in games with multiple strategies |
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Authors: | Tibor Antal Arne Traulsen Corina E Tarnita Martin A Nowak |
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Institution: | a Program for Evolutionary Dynamics, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA b Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA c Max-Planck-Institute for Evolutionary Biology, 24306 Plön, Germany d Department of Value and Decision Science, Tokyo Institute of Technology, Tokyo 152-8552, Japan e PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan |
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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. |
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Keywords: | Evolutionary game theory Finite populations Stochastic effects |
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