Abstract
We consider certain classes of evolutionary selection dynamics in discrete and continuous time and investigate whether strictly dominated strategies can survive in the long run. Two types of results are presented in connection with a class of games containing the game introduced by Dekel and Scotchmer [5]. First, we use an overlapping-generations version of the discrete-time replicator dynamics and establish conditions on the degree of generational overlap for the survival and extinction, respectively, of the strictly dominated strategy in such games. We illustrate these results by means of computer simulations. Second, we show that the strictly dominated strategy may survive in certain evolutionary selection dynamics in continuous time. Journal of Economic Literature Classification Numbers: C72, C73.
We wish to thank Josef Hofbauer, Klaus Ritzberger and Suzanne Scotchmer for helpful comments to earlier drafts of this manuscript. Björnerstedt and Norman thank the Jan Wallander Foundation for financial support.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Akin, “Domination or Equilibrium”, Mathematical Biosciences 50 (1980), 239–250.
J. Björnerstedt and J.W. Weibull, “Nash equilibrium and evolution by imitation”, DELTA WP 93–23, 1993, forthcoming in K. Arrow et al. (eds.), The Rational Foundations of Economic Behavior, Macmillan, 1995.
J. Björnerstedt, “Experimentation, Imitation and Evolutionary Dynamics”, mimeo., Department of Economics, Stockholm University, 1995.
A. Cabrales and J. Sobel, “On the Limit Points of Discrete Selection Dynamics”, J. Econ. Theory 57 (1992), 407–419.
E. Dekel and S. Scotchmer, “On the Evolution of Optimizing Behavior”, J. Econ. Theory 57 (1992), 392–406.
D. Friedman, 1991, “Evolutionary Games in Economics”, Econometrica 59, 637–666.
M. Hirsch and S. Smale, Differential Equations, Dynamic Systems, and Linear Algebra, Academic Press, 1974.
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, 1988.
J.H. Nachbar, “Evolutionary Selection Dynamics in Games: Convergence and Limit Properties”, Int. J. Game Theory 19 (1990), 59–89.
L. Samuelson and J. Zhang, “Evolutionary stability in Asymmetric games”, J. Econ. Theory 57 (1992), 363–391.
L.S. Shapley, “Some Topics in Two-Person Games”, Ann. Math Stud. 5 (1964), 1–28.
J.W. Weibull, Evolutionary Game Theory, MIT Press, Cambridge (USA), 1995.
F. Weissing,”Evolutionary Stability and Dynamic Stability in a Class of Evolutionary Normal Form Games”, in R. Selten (ed.) Game Equilibrium Models: I. Evolution and Game Dynamics, Springer Verlag, Berlin/New York, 1991.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin — Heidelberg
About this chapter
Cite this chapter
Björnerstedt, J., Dufwenberg, M., Norman, P., Weibull, J.W. (1997). Evolutionary Selection Dynamics and Irrational Survivors. In: Albers, W., Güth, W., Hammerstein, P., Moldovanu, B., van Damme, E. (eds) Understanding Strategic Interaction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60495-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-60495-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64430-6
Online ISBN: 978-3-642-60495-9
eBook Packages: Springer Book Archive