Learning in two-dimensional beauty contest games: Theory and experimental evidence

Mikhail Anufriev, John Duffy and Valentyn Panchenko

Journal of Economic Theory, 2022, vol. 201, issue C

Abstract: We extend the beauty contest game to two dimensions: each player chooses two numbers to be as close as possible to certain target values, which are linear functions of the averages of the two number choices. One of the targets depends on the averages of both numbers, making the choices interrelated. We report on an experiment where we vary the eigenvalues of the associated two-dimensional linear system and find that subjects can learn the Pareto-optimal Nash Equilibrium of the system if both eigenvalues are stable and cannot learn it if both eigenvalues are unstable. Interestingly, subjects can also learn it if the system has the saddlepath property – with one stable and one unstable eigenvalue — but only if the one unstable eigenvalue is negative. We show theoretically that our results cannot be explained by homogeneous level-k models where all agents apply the same level k depth of reasoning to their choices, including the naïve learning model. However, our results can be explained by a mixed cognitive-levels model, including the adaptive learning model. We also run a horserace between many models used in the literature with the winner being a simple mixed model with levels 0, 1, and equilibrium reasoning.

Keywords: Learning; Stability; Multivariate systems; Beauty contest; Complexity; Level-k (search for similar items in EconPapers)
JEL-codes: C30 C92 D83 D84 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:201:y:2022:i:c:s0022053122000072

DOI: 10.1016/j.jet.2022.105417

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