Abstract
Stochastic adaptive dynamics require analytical methods and solution concepts that differ in important ways from those used to study deterministic processes. Consider, for example, the notion of asymptotic stability: in a deterministic dynamical system, a state is locally asymptotically stable if any sufficiently small deviation from the original state is self-correcting. We can think of this as a first step toward analysing the effect of stochastic shocks; that is, a state is locally asymptotically stable if, after the impact of a small, one-time shock, the process evolves back to its original state.
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.
Bibliography
Arthur, W.B., Ermoliev, Y. and Kaniovski, Y. 1987. Adaptive growth processes modelled by urn schemes. Kybernetika 6, 49–57; English trans in Cybernetics 23, 779–89.
Benaim, M. and Hirsch, M.W. 1999. Mixed equilibria and dynamical systems arising from fictitious play in perturbed games. Games and Economic Behavior 29, 36–72.
Bergin, J. and Lipman, B.L. 1996. Evolution with state-dependent mutations. Econometrica 64, 943–56.
Binmore, K., Samuelson, L. and Young, H.P. 2003. Equilibrium selection in bargaining models. Games and Economic Behavior 45, 296–328.
Blume, L.E. 1995. The statistical mechanics of best-response strategy revision. Games and Economic Behavior 11, 111–45.
Blume, L.E. 2003. How noise matters. Games and Economic Behavior 44, 251–71.
Bowles, S. 2004. Microeconomics: Behavior, Institutions, and Evolution. Princeton, NJ: Princeton University Press.
Ellison, G. 1993. Learning, local interaction, and coordination. Econometrica 61, 1047–71.
Ellison, G. 2000. Basins of attraction, long run equilibria, and the speed of step-by-step evolution. Review of Economic Studies 67, 17–45.
Foster, D. and Young, H.P. 1990. Stochastic evolutionary game dynamics. Theoretical Population Biology 38, 219–32.
Freidlin, M. and Wentzell, A. 1984. Random Perturbations of Dynamical Systems. Berlin: Springer-Verlag.
Fudenberg, D. and Kreps, D. 1993. Learning mixed equilibria. Games and Economic Behavior 5, 320–67.
Haken, H. 1978. Synergetics. Berlin: Springer-Verlag.
Harsanyi, J. and Selten, R. 1988. A General Theory of Equilibrium Selection in Games. Cambridge MA: MIT Press.
Hofbauer, J. and Sandholm, W. 2002. On the global convergence of stochastic fictitious play. Econometrica 70, 2265–94.
Kandori, M., Mailath, G. and Rob, R. 1993. Learning, mutation, and long-run equilibria in games. Econometrica 61, 29–56.
Kandori, M. and Rob, R. 1995. Evolution of equilibria in the long run: a general theory and applications. Journal of Economic Theory 65, 383–414.
Kaniovski, Y. and Young, H.P. 1995. Learning dynamics in games with stochastic perturbations. Games and Economic Behavior 11, 330–63.
Karlin, S. and Taylor, H.M. 1975. A First Course in Stochastic Processes. New York: Academic Press.
Vega-Redondo, F. 1997. The evolution of Walrasian behaviour. Econometrica 65, 375–84.
Young, H.P. 1993a. The evolution of conventions. Econometrica 61, 57–84.
Young, H.P. 1993b. An evolutionary model of bargaining. Journal of Economic Theory 59, 145–68.
Young, H.P. 1998a. Conventional contracts. Review of Economic Studies 65, 776–92.
Young, H.P. 1998b. Individual Strategy and Social Structure. Princeton. NJ: Princeton University Press.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Copyright information
© 2010 Palgrave Macmillan, a division of Macmillan Publishers Limited
About this chapter
Cite this chapter
Durlauf, S.N., Blume, L.E. (2010). Stochastic Adaptive Dynamics. In: Durlauf, S.N., Blume, L.E. (eds) Game Theory. The New Palgrave Economics Collection. Palgrave Macmillan, London. https://doi.org/10.1057/9780230280847_34
Download citation
DOI: https://doi.org/10.1057/9780230280847_34
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-0-230-23890-9
Online ISBN: 978-0-230-28084-7
eBook Packages: Palgrave Media & Culture CollectionLiterature, Cultural and Media Studies (R0)