Bulletin of Mathematical Biology

, Volume 66, Issue 6, pp 1621–1644

Evolutionary game dynamics in finite populations

  • Christine Taylor
  • Drew Fudenberg
  • Akira Sasaki
  • Martin A. Nowak

DOI: 10.1016/j.bulm.2004.03.004

Cite this article as:
Taylor, C., Fudenberg, D., Sasaki, A. et al. Bull. Math. Biol. (2004) 66: 1621. doi:10.1016/j.bulm.2004.03.004


We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.

Copyright information

© Society for Mathematical Biology 2004

Authors and Affiliations

  • Christine Taylor
    • 1
  • Drew Fudenberg
    • 2
  • Akira Sasaki
    • 3
  • Martin A. Nowak
    • 4
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of EconomicsHarvard UniversityCambridgeUSA
  3. 3.Faculty of Science, Department of BiologyKyushu UniversityFukuokaJapan
  4. 4.Program for Evolutionary DynamicsHarvard UniversityCambridgeUSA

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