Monotone Imitation Dynamics in Large Populations

26 Pages Posted: 16 Nov 2007

See all articles by Drew Fudenberg

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Lorens A. Imhof

RWTH Aachen University - Institute of Statistics

Date Written: November 2007

Abstract

We analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the aspiration-and-imitation process of Binmore and Samuelson [3] and the related processes proposed by Benaïm and Weibull [2] and Traulsen et al. [24], as well as the frequency-dependent Moran process studied by Fudenberg et al. [15]. We illustrate our results by considering the effect of the number of periods of repetition on the selected equilibrium in repeated play of the prisoner's dilemma when players are restricted to a small set of simple strategies.

Keywords: Equilibrium selection, Learning model, Limit distribution, Markov process, Prisoner's dilemma

JEL Classification: C62, C72, C73

Suggested Citation

Fudenberg, Drew and Imhof, Lorens A., Monotone Imitation Dynamics in Large Populations (November 2007). Harvard Institute of Economic Research Discussion Paper No. 2141. Available at SSRN: https://ssrn.com/abstract=1029691 or http://dx.doi.org/10.2139/ssrn.1029691

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

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

Lorens A. Imhof

RWTH Aachen University - Institute of Statistics ( email )

Aachen, D-52056
Germany

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