Planar Beauty Contests

Mikhail Anufriev, John Duffy and Valentyn Panchenko

No 2019-06, Discussion Papers from School of Economics, The University of New South Wales

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, a', as in a standard beauty contest game, the realization of b depends on both a' and on the average forecast for b, 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 cognitive theory (search for similar items in EconPapers)
JEL-codes: C30 C92 D83 D84 (search for similar items in EconPapers)
Pages: 88 pages
New Economics Papers: this item is included in nep-exp and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Working Paper: Planar Beauty Contests (2019)
Working Paper: Planar Beauty Contests (2019)
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