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Deterministic Approximation of Stochastic Evolution in Games

Michel Benaim and Jörgen Weibull
Additional contact information
Michel Benaim: Université de Cergy-Pontiose, Postal: Department of Mathematics, 2 Avenue Adolphe Chauvin, F-953 02 Cergy-Pontoise, Cedex, France

No 534, Working Paper Series from Research Institute of Industrial Economics

Abstract: This paper provides deterministic approximation results for stochastic processes that arise when finite populations recurrently play finite games. The deterministic approximation is defined in continuous time as 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 solution through the initial state of the stochastic process at some point in time enters a basin of attraction, then the stochastic process will enter any given neighborhood of that attractor within a finite and deterministic time with a probability that exponentially approaches one as the population size goes to infinity. The process will remain in this neighborhood for a random time that almost surely exceeds an exponential function of the population size. During this time interval, the process spends almost all time at a certain subset of the attractor, its so-called Birkhoff center. We sharpen this result in the special case of ergodic processes.

Keywords: Game Theory; Evolution; Approximation (search for similar items in EconPapers)
JEL-codes: C70 C72 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2000-06-19, Revised 2001-10-30
New Economics Papers: this item is included in nep-evo
References: Add references at CitEc
Citations: View citations in EconPapers (8)

Published in Econometrica, 2003, pages 873-903.

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Journal Article: Deterministic Approximation of Stochastic Evolution in Games (2003)
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