Learning Dynamics, Lock-In, and Equilibrium Selection in Experimental Coordination Games

UCSD Economics Discussion Paper 97-19

51 Pages Posted: 3 Apr 1998

See all articles by Vincent P. Crawford

Vincent P. Crawford

University of California, San Diego (UCSD) - Department of Economics; University of Oxford - Department of Economics

Date Written: August 1997

Abstract

This paper compares the leading theoretical approaches to equilibrium selection, both traditional and adaptive, in the light of recent experiments by Van Huyck, Battalio, and Beil (henceforth "VHBB") in which subjects repeatedly played coordination games, uncertain only about each other's strategy choices. The large strategy spaces of VHBB's designs and the variety of interaction patterns they considered yielded rich dynamics, with systematic differences in limiting outcomes across treatments. Explaining these differences promises to shed considerable light on equilibrium selection and coordination more generally, in the field as well as the laboratory. Following earlier analyses by Bruno Broseta and myself, I propose a model that gives a flexible characterization of individual behavior and allows for strategic uncertainty, in the form of idiosyncratic random shocks to players' adjustments. The model includes representatives of the leading approaches to equilibrium selection, which are distinguished by different values of behavioral parameters, including variances that represent the level of strategic uncertainty. The model provides a framework within which to estimate the parameters econometrically, using data from the experiments. The estimates suggest that VHBB's treatments evoked high initial levels of strategic uncertainty, declining steadily to zero as subjects learned to predict each other's responses. The resulting model has nonstationary transition probabilities and history-dependent dynamics that lock in on an equilibrium of the stage game, whose prior probability distribution is nondegenerate due to persistent effects of strategic uncertainty. The analysis shows that even when strategic uncertainty is eventually eliminated by learning, it imparts a drift to the learning dynamics, whose magnitude and direction depend on the environment and the behavioral parameters. This drift makes the distribution of the limiting outcome vary across treatments much as its empirical frequency distribution varied in the experiments. In this sense, taking the persistent effects of strategic uncertainty into account allows a simple, unified explanation of VHBB's results.

JEL Classification: C70, C91, D83

Suggested Citation

Crawford, Vincent P., Learning Dynamics, Lock-In, and Equilibrium Selection in Experimental Coordination Games (August 1997). UCSD Economics Discussion Paper 97-19, Available at SSRN: https://ssrn.com/abstract=73488 or http://dx.doi.org/10.2139/ssrn.73488

Vincent P. Crawford (Contact Author)

University of California, San Diego (UCSD) - Department of Economics ( email )

Department of Economics
9500 Gilman Drive
La Jolla, CA 92093-0508
United States
302-729-3230 (Phone)

HOME PAGE: http://econweb.ucsd.edu/~v2crawford/

University of Oxford - Department of Economics ( email )

All Souls College
Oxford, Oxfordshire OX1 4AL
United Kingdom
+44-1865-279339 (Phone)

HOME PAGE: http://econweb.ucsd.edu/~v2crawford/

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