This paper provides deterministic approximation results for stochastic processes that arise when finite populations of boundedly rational agents recurrently play finite games. The deterministic approximation is defined in continuous time in terms of a system of ordinary differential equations of the type studied in evolutionary game theory. We establish precise connections between the long-run behavior of the stochastic process, for large populations, and its deterministic approximation. In particular, we show that if the deterministic flow enters a basin of attraction, then the stochastic process follows this flow closely until this (deterministic) entry time, with a probability that approaches one exponentially in the population size. After entry, the process remains in a neighborhood of the attractor for a random time span that exceeds an exponential function of the population size. The process spends almost all this time in a neighborhood of a subset of the attractor, the Birkhoff center of the flow restricted to the attractor.
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Length: 37 pages Date of creation: 2000 Date of revision: Handle: RePEc:fth:iniesr:534
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Find related papers by JEL classification: C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
References listed on IDEAS Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
Fudenberg, D. & Kreps, D.M., 1992.
"Learning Mixed Equilibria,"
Working papers
92-13, Massachusetts Institute of Technology (MIT), Department of Economics.
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Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.) This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.