Abstract
The evolutionary dynamics of bimatrix games is studied for rescaled partnership games and zero sum games. The former case leads to gradient systems. The selection equations for sexual and asexual reproduction of genotypes corresponding to mixed strategies are analysed. As examples, the origin of anisogamy and cyclic chases for predator-prey coevolution are studied.
Similar content being viewed by others
References
Akin, E.: The geometry of population genetics. Lect. Notes Biomath. 31. Berlin Heidelberg New York: Springer 1979
Bell. G.: The evolution of anisogamy. J. Theor. Biol. 73, 247–270 (1978)
Bomze, I., Schuster, P., Sigmund, K.: The role of mendelian genetics in strategic models of animal behaviour. J. Theor. Biol. 101, 19–38 (1983)
Charlesworth, B.: The population genetics of anisogamy. J. Theor. Biol. 73, 347–357 (1978)
Dawkins, R.: The selfish gene. Oxford: Oxford University Press 1976
Eshel, I.: Evolutionarily stable strategies and viability selection in mendelian populations. Theor. Popul. Biol. 22, 204–217 (1982)
Hammerstein, P.: The role of asymmetries in animal contests. Anm. Behav. 29, 193–205 (1979)
Hammerstein, P., Parker, G.: The asymmetric war of attrition. J. Theor. Biol. 96, 647–682 (1982)
Hoekstra, R.: On the asymmetry of sex: evolution of mating types in isogamous populations. J. Theor. Biol. 98, 427–451 (1982)
Hofbauer, J.: Are there mixed ESS in asymmetric games. To appear (1987)
Knowlton, N.: A note on the evolution of gamete dimorphism. J. Theor. Biol. 46, 283–285 (1974)
Maynard Smith, J.: Parental Investment: A prospective analysis. Anm. Behav. 25, 1–9 (1977)
Maynard Smith, J.: The evolution of sex. Cambridge: Cambridge University Press 1978
Maynard Smith, J.: Evolution and the theory of games. Cambridge: Cambridge University Press 1982
Parker, G.: Assessment strategy and the evolution of animal conflicts. J. Theor. Biol. 47, 223–243 (1974)
Parker, G.: Selection in non-random fusion of gametes during the evolution of anisogamy. J. Theor. Biol. 73, 1–28 (1978)
Parker, G., Barker, R., Smith, V.: The origin and evolution of gamete dimorphism and the male-female-phenomenon. J. Theor. Biol. 36, 529–553 (1977)
Schuster, P., Sigmund, K.: A note on the evolution of sexual dimorphism. J. Theor. Biol. 94, 107–110 (1982)
Schuster, P., Hof bauer, J., Sigmund, K., Wolff, R.: Selfregulation of behaviour in animal societies II. Biol. Cybern. 40, 9–16 (1983)
Selten, R.: A note on evolutionarily stable strategies in asymmetrical animal conflicts. J. Theor. Biol. 84, 93–101 (1980)
Shahshahani, S.: A new mathematical framework for the study of linkage and selection. Memoirs AMS 211 (1979)
Sigmund, K.: Game dynamics, mixed strategies and gradient systems. Theor. Popul. Biol. 32, 114–126 (1987)
Sigmund, K.: A maximum principle for frequency dependent selection. To appear in: Math. Biosci. (1987)
Stewart, F.: Evolution of dimorphism in a predator-prey model. Theor. Popul. Biol. 2, 493–506 (1971)
Taylor, P.: Evolutionarily stable strategies with two types of players. J. Appl. Probab. 16, 76–83 (1979)
Taylor, P., Jonker, L.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Koth, M., Sigmund, K. Gradients for the evolution of bimatrix games. J. Math. Biology 25, 623–635 (1987). https://doi.org/10.1007/BF00275498
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00275498