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Three characterizations of population strategy stability

  • W. G. S. Hines (a1)


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.


Corresponding author

Postal address: Department of Mathematics and Statistics, University of Guelph, Guelph, Ont., Canada N1G 2W1.


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Research supported by NRC Operating Grant A6187.



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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.


Three characterizations of population strategy stability

  • W. G. S. Hines (a1)


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