Skip to main content
×
×
Home

Three characterizations of population strategy stability

  • W. G. S. Hines (a1)
Abstract

In addition to the concept of the evolutionarily stable strategy (ESS), developed specifically for considering intraspecific conflicts, concepts such as the Nash equilibrium from game theory and the attractor or sink from dynamical systems theory appear relevant to the problem of characterizing populations of stable composition. The three concepts mentioned are discussed for one simple standard population model. It is found that evolutionarily stable strategies of one type are necessarily Nash equilibrium strategies, although the converse is not true. The dynamical systems characterization is found to provide a model for populations susceptible to invasion by ‘co-operative' strategies, but capable of evolving back in average to the original equilibrium.

Copyright
Corresponding author
Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ont., Canada N1G 2W1.
Footnotes
Hide All

Research supported by NRC Operating Grant A6187.

Footnotes
References
Hide All
Auslander, D. J., Guckenheimer, J. M. and Oster, G. (1978) Random evolutionary stable strategies. Theoret. Population Biol. 13, 276293.
Casti, J. L. (1977) Dynamical Systems and their Applications. Academic Press, New York.
Friedman, A. (1971) Differential Games. Wiley, New York.
Haigh, J. (1975) Game theory and evolution (abstract). Adv. Appl. Prob. 7, 811.
Hines, W. G. S. (1978) Mutations and stable strategies. J. Theoret. Biol. 72, 413428.
Hines, W. G. S. (1980) Strategy stability in complex populations. J. Appl. Prob. 17(3).
Hirsch, M. and Smale, S. (1974) Differential Equations, Dynamical Systems and Linear Algebra. Academic Press, New York.
Hirschleifer, J. and Riley, J. G. (1978) Elements of the theory of auctions and contests. UCLA Economics Department Working Paper No. 118.
Maynard Smith, J. (1974) The theory of games and the evolution of animal conflicts. J. Theoret. Biol. 47, 209221.
Mirmirani, M. and Oster, G. (1978) Competition, kin selection and evolution. Theoret. Population Biol. 13, 304339.
Riley, J. G. (1978) Evolutionary equilibrium strategies. J. Theoret. Biol. 76, 109123.
Taylor, P. D. and Jonker, L. B. (1978) Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145156.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 7 *
Loading metrics...

Abstract views

Total abstract views: 107 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 16th August 2018. This data will be updated every 24 hours.