Journal of Mathematical Biology

, Volume 29, Issue 6, pp 513–529 | Cite as

The dynamical attainability of ESS in evolutionary games

  • T. Takada
  • J. Kigami


In this paper, the attainability of ESS of the evolutionary game among n players under the frequency-independent selection is studied by means of a mathematical model describing the dynamical development and a concept of stability (strongly determined stability). It is assumed that natural selection and small mutations cause the phenotype to change gradually in the direction of fitness increasing. It is shown that (1) the ESS solution is not always evolutionarily attainable in the evolutionary dynamics, (2) in the game where the interaction between two species is completely competitive, the Nash solution is always attainable, and (3) one of two species may attain the state of minimum fitness as a result of evolution. The attainability of ESS is also examined in two game models on the sex ratio of wasps and aphids in light of our criterion of the attainability of ESS.

Key words

Evolutonary game Dynamical attainability of ESS Strongly determined stability 


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • T. Takada
    • 1
  • J. Kigami
    • 2
  1. 1.Department of BiophysicsKyoto UniversityKyotoJapan
  2. 2.Department of MathematicsKyoto UniversityKyotoJapan
  3. 3.School of International Cultural RelationsHokkaido Tokai UniversityMinami-ku, SapporoJapan
  4. 4.Division of System Science, Graduate School of Science & TechnologyKobe UniversityKobeJapan

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