Stochastic Stability in Large Populations

53 Pages Posted: 20 Jul 2009

See all articles by Drew Fudenberg

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Daniel Hojman

Harvard University - Harvard Kennedy School (HKS)

Date Written: July 10, 2009

Abstract

Most work in evolutionary game theory analyzes a deterministic adjustment process on a continuum of agents. However, both the assumption of a continuum and that of no randomness are approximations, so it is important to study the behavior of adjustment processes on a large but finite population subject to small but persistent stochastic shocks. This paper characterizes the properties of the invariant distribution of birth-death processes in the double limit as the population becomes infinitely large and the perturbation vanishingly small. We show that the order of these limits does not change the conclusions for processes with 'strong basins,' which is the case when the unperturbed process is deterministic. In contrast, the order of limits does matter for processes with 'weak basins,' where the unperturbed process is stochastic except at a finite number of points.

Keywords: equilibrium selection, stochastic stability, large deviations

JEL Classification: C62, C73

Suggested Citation

Fudenberg, Drew and Hojman, Daniel A., Stochastic Stability in Large Populations (July 10, 2009). Harvard Institute of Economic Research Discussion Paper No. 2177. Available at SSRN: https://ssrn.com/abstract=1435492 or http://dx.doi.org/10.2139/ssrn.1435492

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Daniel A. Hojman

Harvard University - Harvard Kennedy School (HKS) ( email )

79 John F. Kennedy Street
Cambridge, MA 02138
United States
617-384-8120 (Phone)
617-496-5747 (Fax)

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