Learning in Two-Dimensional Beauty Contest Games: Theory and Evidence

88 Pages Posted: 20 Jun 2019 Last revised: 11 Sep 2021

See all articles by Mikhail Anufriev

Mikhail Anufriev

University of Technology Sydney (UTS)

John Duffy

University of California, Irvine

Valentyn Panchenko

UNSW Business School, Economics, University of New South Wales

Date Written: June 12, 2019

Abstract

We introduce a planar beauty contest game where agents must simultaneously guess two, endogenously determined variables, a and b. The system of equations determining the actual values of a and b is a coupled system; while the realization of a depends on the average forecast for a, as in a standard beauty contest game, the realization of b depends on both the average forecasts for a and for b. Our aim is to better understand the conditions under which agents learn the steady state of such systems and whether the eigenvalues of the system matter for the convergence or divergence of this learning process. We find that agents are able to learn the steady state of the system when the eigenvalues are both less than 1 in absolute value (the sink property) or when the steady state is saddlepath stable with the one root outside the unit circle being negative. By contrast, when the steady state exhibits the source property (two unstable roots) or is saddlepath stable with the one root outside the unit circle being positive, subjects are unable to learn the steady state of the system. We show that these results can be explained by either an adaptive learning model or a mixed cognitive levels model, while other approaches, e.g., naive or homogeneous level-k learning, do not consistently predict whether subjects converge
to or diverge away from the steady state.

Keywords: Beauty Contest, Learning, Stability, Simultaneous Equation Systems, Level-k theory, Cognitive hierarchy model, Experimental Economics

JEL Classification: C30, C92, D83, D84

Suggested Citation

Anufriev, Mikhail and Duffy, John and Panchenko, Valentyn, Learning in Two-Dimensional Beauty Contest Games: Theory and Evidence (June 12, 2019). UNSW Business School Research Paper Forthcoming, Available at SSRN: https://ssrn.com/abstract=3404334 or http://dx.doi.org/10.2139/ssrn.3404334

Mikhail Anufriev

University of Technology Sydney (UTS) ( email )

P. O. Box 123
Broadway, NSW 2007
Australia

John Duffy (Contact Author)

University of California, Irvine ( email )

Department of Economics
3151 Social Science Plaza
Irvine, CA 92697
United States
949-824-8341 (Phone)

Valentyn Panchenko

UNSW Business School, Economics, University of New South Wales ( email )

Sydney, NSW 2052
Australia

HOME PAGE: http://research.economics.unsw.edu.au/vpanchenko

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