Abstract
For the analysis of the dynamics of game playing populations, it is common practice to assume infinitely large populations. Infinite models yield predictions of fixed points and their stability properties. However, these models cannot demonstrate the influence of genetic drift, caused by stochastic sampling in small populations. Instead, we propose Markov models of finite populations for the analysis of genetic drift in games. With these exact models, we can study the stability of evolutionary stable strategies, and measure the influence of genetic drift in the long run. We show that genetic drift can introduce significant differences in the expectations of long term behavior.
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References
Weibull, J.W.: Evolutionary Game Theory. MIT Press, Cambridge (1995)
Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (1998)
Nowak, M.A., Sigmund, K.: Evolutionary dynamics of biological games. Science 303, 793–799 (2004)
Vose, M.D.: The Simple Genetic Algorithm. MIT Press, Cambridge (1999)
Fischer, R.A.: The Genetical Theory of Natural Selection. Clarendon, Oxford (1930)
Wright, S.: Evolution in mendelian populations. Genetics 16, 97–159 (1931)
Nix, A.E., Vose, M.D.: Modelling genetic algorithms with markov chains. Annals of Mathematics and Artificial Intelligence, 79–88 (1992)
Liekens, A.M.L., ten Eikelder, H.M.M., Hilbers, P.A.J.: Modeling and simulating diploid simple genetic algorithms. In: FOGA VII (2003)
Kimura, M.: The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (1986)
Fogel, D.B., Fogel, G.B.: Evolutionary stable strategies are not always stable under evolutionary dynamics. In: Evolutionary Programming IV, pp. 565–577 (1995)
Fogel, D.B., Fogel, G.B., Andrews, P.C.: On the instability of evolutionary stable strategies. BioSystems 44, 135–152 (1997)
Fogel, G.B., Andrews, P.C., Fogel, D.B.: On the instability of evolutionary stable strategies in small populations. Ecological Modelling 109, 283–294 (1998)
Ficici, S.G., Pollack, J.B.: Effects of finite populations on evolutionary stable strategies. In: Proceedings of the 2000 Genetic and Evolutionary Computation Conference (2000)
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© 2004 Springer-Verlag Berlin Heidelberg
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Liekens, A.M.L., ten Eikelder, H.M.M., Hilbers, P.A.J. (2004). Predicting Genetic Drift in 2×2 Games. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24854-5_57
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DOI: https://doi.org/10.1007/978-3-540-24854-5_57
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22344-3
Online ISBN: 978-3-540-24854-5
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