Abstract
Economic systems often involve large numbers of agents whose behaviour, and patterns of interaction, have stochastic components. The dynamic properties of such systems can be analysed using stochastic dynamical systems theory. A key feature of these processes is that their long-run behaviour often differs substantially from the behaviour of the deterministic process obtained by taking expectations of the random variables. Furthermore, unlike the deterministic dynamics, the theory yields sharp predictions about the probability of being in different equilibria independently of the initial conditions.
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
Bibliography
Arthur, W.B., Y. Ermoliev, and Y. Kaniovski. 1987. Adaptive growth processes modelled by urn schemes. Kybernetika 6: 49–57; English trans in Cybernetics 23: 779–789.
Benaim, M., and M.W. Hirsch. 1999. Mixed equilibria and dynamical systems arising from fictitious play in perturbed games. Games and Economic Behavior 29: 36–72.
Bergin, J., and B.L. Lipman. 1996. Evolution with state-dependent mutations. Econometrica 64: 943–956.
Binmore, K., L. Samuelson, and H.P. Young. 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: 111–145.
Blume, L.E. 2003. How noise matters. Games and Economic Behavior 44: 251–271.
Bowles, S. 2004. Microeconomics: Behavior, institutions, and evolution. Princeton: Princeton University Press.
Ellison, G. 1993. Learning, local interaction, and coordination. Econometrica 61: 1047–1071.
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 H.P. Young. 1990. Stochastic evolutionary game dynamics. Theoretical Population Biology 38: 219–232.
Freidlin, M., and A. Wentzell. 1984. Random perturbations of dynamical systems. Berlin: Springer-Verlag.
Fudenberg, D., and D. Kreps. 1993. Learning mixed equilibria. Games and Economic Behavior 5: 320–367.
Haken, H. 1978. Synergetics. Berlin: Springer-Verlag.
Harsanyi, J., and R. Selten. 1988. A general theory of equilibrium selection in games. Cambridge, MA: MIT Press.
Hofbauer, J., and W. Sandholm. 2002. On the global convergence of stochastic fictitious play. Econometrica 70: 2265–2294.
Kandori, M., and R. Rob. 1995. Evolution of equilibria in the long run: A general theory and applications. Journal of Economic Theory 65: 383–414.
Kandori, M., G. Mailath, and R. Rob. 1993. Learning, mutation, and long-run equilibria in games. Econometrica 61: 29–56.
Kaniovski, Y., and H.P. Young. 1995. Learning dynamics in games with stochastic perturbations. Games and Economic Behavior 11: 330–363.
Karlin, S., and H.M. Taylor. 1975. A first course in stochastic processes. New York: Academic.
Vega-Redondo, F. 1997. The evolution of Walrasian behaviour. Econometrica 65: 375–384.
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: 145–168.
Young, H.P. 1998a. Conventional contracts. Review of Economic Studies 65: 776–792.
Young, H.P. 1998b. Individual strategy and social structure. Princeton: Princeton University Press.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Young, H.P. (2018). Stochastic Adaptive Dynamics. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1990
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_1990
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences