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.
Highlights
Evolutionary game theory is the study of frequency dependent selection (Maynard Smith and Price, 1973; Maynard Smith, 1982; Hofbauer and Sigmund, 1998, 2003; Nowak and Sigmund, 2004)
We study the case of weak selection
We have studied evolutionary game dynamics in well-mixed populations with n strategies
Summary
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Tibor Antal a , Arne Traulsen b , Hisashi Ohtsuki c , Corina E. Nowak a a Program for Evolutionary Dynamics, Department of Mathematics, Department of Organismic and Evolutionary Biology, Harvard University, Cambridge MA 02138, USA b Max-Planck-Institute t p for Evolutionary Biology, 24306 Plön, Germany i r c c Department of Value and Decision Science, Tokyo Institute of Technology, Tokyo 1528552; PRESTO, Japan Science and Technology Agency, Saitama 332-0012, Japan s u
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