Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-06T05:02:53.772Z Has data issue: false hasContentIssue false
  • English
  • Français

On learning and the evolutionarily stable strategy

Published online by Cambridge University Press:  14 July 2016

W. G. S. Hines  and
D. T. Bishop
W. G. S. Hines*
Affiliation:
University of Guelph
D. T. Bishop*
Affiliation:
LDS Hospital, Salt Lake City
*
∗ Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1.
∗∗ Department of Medical Biophysics and Computing, LDS Hospital, 325 8th Avenue, Salt Lake City, UT 84143, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

In evolutionarily stable strategy models, transmission of one's strategy to one's offspring has routinely been assumed to be exact, whether this transmission is genetic or by instruction. If inexact transmission of strategy is possible, however, the nature of the mode of transmission becomes important. This paper demonstrates analytically that the possibility of learning one's strategy can increase rather than decrease eventual strategy diversity and that the resulting population mean strategy can differ appreciably from an evolutionarily stable strategy. These results are found to be consistent with simulation results reported in the literature.

Keywords

ANIMAL CONFLICT MODELSDEVELOPMENTALLY STABLE STRATEGYGAME DYNAMICSLEARNING BEHAVIOURLEARNING RULEPOPULATION DYNAMICSPOPULATION STRATEGY STABILITYSTRATEGY LEARNING
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 3 , September 1983 , pp. 689 - 695
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akin, E. (1983) Exponential families and game dynamics. Canad. J. Math. Google Scholar
Dawkins, R. (1980) In Sociobiology — Beyond Nature/Nurture?, ed. Barlow, G. W. and Silverberg, J., Westview Press, Boulder, Co. Google Scholar
Harley, C. B. (1981) Learning the evolutionarily stable strategy. J. Theoret. Biol. 89, 611–633.Google Scholar
Hines, W. G. S. (1978) Mutations and stable strategies. J. Theoret. Biol. 72, 413–428.Google Scholar
Hines, W. G. S. (1980a) An evolutionarily stable strategy model for randomly mating diploid populations. J. Theoret. Biol. 87, 379–384.CrossRefGoogle ScholarPubMed
Hines, W. G. S. (1980b) Strategy stability in complex populations. J. Appl. Prob. 17, 600–610.Google Scholar
Hines, W. G. S. (1982a) Mutations, perturbations and evolutionarily stable strategies. J. Appl. Prob. 19, 204–209.CrossRefGoogle Scholar
Hines, W. G. S. (1982b) Strategy stability in complex randomly mating diploid populations. J. Appl. Prob. 19, 653–659.CrossRefGoogle Scholar
Hines, W. G. S. and Bishop, D. T. (1983) Evolutionarily stable strategies in diploid populations with general inheritance patterns. J. Appl. Prob. 20, 395–399.Google Scholar
Lloyd, D. G. (1977) Genetic and phenotypic models of natural selection. J. Theoret. Biol. 69, 543–560.Google Scholar
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209–221.Google Scholar
Maynard Smith, J. (1981) Will a sexual population evolve to an ESS? Amer. Natur. 117, 1015–1018.Google Scholar
Treisman, M. (1981) Evolutionary limits to the frequency of aggression between related or unrelated conspecifics in diploid species with simple Mendelian inheritance. J. Theoret. Biol. 93, 97–124.Google Scholar
Zeeman, E. C. (1980) Population dynamics from game theory. In Global Theory of Dynamical Systems, Proceedings, Northwestern, 1979, Springer-Verlag, Berlin, 471–479.Google Scholar