Mutation-selection equilibrium in games with multiple strategies

Tibor Antal, Arne Traulsen, Hisashi Ohtsuki, Corina E. Tarnita, Martin A. Nowak

Research output: Contribution to journalArticlepeer-review

115 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)614-622
Number of pages9
JournalJournal of Theoretical Biology
Issue number4
StatePublished - Jun 21 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Immunology and Microbiology
  • Applied Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Agricultural and Biological Sciences
  • Statistics and Probability
  • Modeling and Simulation


  • Evolutionary game theory
  • Finite populations
  • Stochastic effects


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