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The invisible hand of Laplace: The role of market structure in price convergence and oscillation

Rabani, Yuval and Schulman, Leonard J. (2021) The invisible hand of Laplace: The role of market structure in price convergence and oscillation. Journal of Mathematical Economics, 95 . Art. No. 102475. ISSN 0304-4068. doi:10.1016/j.jmateco.2021.102475. https://resolver.caltech.edu/CaltechAUTHORS:20210128-142707495

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Abstract

The “invisible hand” of the free market is remarkably effective at producing near-equilibrium prices. This is difficult to quantify, however, in the absence of an agreed model for out-of-equilibrium trade. Short of a fully reductionist model, a useful substitute would be a scaling law relating equilibration time and other market parameters. Even this, however, is missing in the literature. We make progress in this direction. We examine a class of Arrow–Debreu markets with price signaling driven by continuous-time proportional-tâtonnement. We show that the connectivity among the participants in the market determines quite accurately a scaling law for convergence time of the market to equilibrium, and thus determines the effectiveness of the price signaling. To our knowledge this is the first characterization of price stability in terms of market connectivity. At a technical level, we show how convergence in our class of markets is determined by a market-dependent Laplacian matrix. If a market is not isolated but, rather, subject to external noise, equilibrium theory has predictive value only to the extent to which that noise is counterbalanced by the price equilibration process. Our model quantifies this predictive value by providing a scaling law that relates the connectivity of the market with the variance of its prices.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.jmateco.2021.102475DOIArticle
https://arxiv.org/abs/1602.07628arXivDiscussion Paper
ORCID:
AuthorORCID
Schulman, Leonard J.0000-0001-9901-2797
Additional Information:© 2021 Elsevier. Received 25 June 2020, Revised 11 December 2020, Accepted 14 January 2021, Available online 28 January 2021. YR was supported in part by ISF grant 856-11, BSF grant 2012333 and I-CORE Algo. LJS was supported in part by National Science Foundation grants 1319745, 1618795, 1909972; Binational Science Foundation grant 2012333; and, during a residency at the Israel Institute for Advanced Studies, by a EURIAS Senior Fellowship co-funded by the European Marie Skłodowska-Curie Actions under the 7th Framework Programme. Thanks to John Ledyard, Federico Echenique, Umesh Vazirani, Joel Sobel, Andrew Stuart, Franca Hoffmann and Jenish Mehta for their insights. An early draft of some of this work was posted at ArXiv:1602.07628. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Funders:
Funding AgencyGrant Number
Israel Science Foundation856-11
Binational Science Foundation (USA-Israel)2012333
I-CORE Program of the Planning and Budgeting CommitteeUNSPECIFIED
NSFCCF-1319745
NSFCCF-1618795
NSFCCF-1909972
Israel Institute for Advanced StudiesUNSPECIFIED
European Institutes for Advanced Study (EURIAS)UNSPECIFIED
Marie Curie FellowshipUNSPECIFIED
Subject Keywords:Disequilibrium dynamics; Arrow-Debreu model; Tâtonnement; Fluctuation-dissipation theorem; Graph expansion; Graph spectrum
DOI:10.1016/j.jmateco.2021.102475
Record Number:CaltechAUTHORS:20210128-142707495
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210128-142707495
Official Citation:Yuval Rabani, Leonard J. Schulman, The invisible hand of Laplace: The role of market structure in price convergence and oscillation, Journal of Mathematical Economics, Volume 95, 2021, 102475, ISSN 0304-4068, https://doi.org/10.1016/j.jmateco.2021.102475.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107792
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Jan 2021 22:38
Last Modified:19 Aug 2021 21:33

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