Random Matching in Adaptive Dynamics

26 Pages Posted: 13 Dec 2006

See all articles by Glenn Ellison

Glenn Ellison

Massachusetts Institute of Technology (MIT) - Department of Economics; National Bureau of Economic Research (NBER)

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Lorens A. Imhof

RWTH Aachen University - Institute of Statistics

Date Written: December 2006

Abstract

This paper studies the effect of randomness in per-period matching on the long-run outcome of non-equilibrium adaptive processes. If there are many matchings between each strategy revision, the randomness due to matching will be small; our question is when a very small noise due to matching has a negligible effect. We study two different senses of this idea, and provide sufficient conditions for each. The less demanding sense corresponds to sending the matching noise to zero while holding fixed all other aspects of the adaptive process. The second sense in which matching noise can be negligible is that it doesn't alter the limit distribution obtained as the limit of the invariant distributions as an exogeneous "mutation rate" goes to zero. When applied to a model with mutations, the difference between these two senses is in the order of limits: the first sense asks for continuity of e.g. the ergodic distribution in the matching noise holding the mutation rate fixed, whereas the second sense asks for continuity of the limit distribution in the matching noise.

Suggested Citation

Ellison, Glenn David and Fudenberg, Drew and Imhof, Lorens A., Random Matching in Adaptive Dynamics (December 2006). Harvard Institute of Economic Research Discussion Paper No. 2126. Available at SSRN: https://ssrn.com/abstract=951469 or http://dx.doi.org/10.2139/ssrn.951469

Glenn David Ellison

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-380B
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617-253-8702 (Phone)

National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
United States

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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