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Convergence of incentive-driven dynamics in Fisher markets

Dvijotham, Krishnamurthy and Rabani, Yuval and Schulman, Leonard J. (2022) Convergence of incentive-driven dynamics in Fisher markets. Games and Economic Behavior, 134 . pp. 361-375. ISSN 0899-8256. doi:10.1016/j.geb.2020.11.005. https://resolver.caltech.edu/CaltechAUTHORS:20201217-133744650

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Abstract

We study out-of-equilibrium price dynamics in Fisher markets. We develop a general framework in which sellers have (a) a set of atomic price update rules (APU), which are simple responses to a price vector; (b) a belief-formation procedure that simulates actions of other sellers (themselves using the APU) to some finite horizon in the future. Sellers use an APU to respond to a price vector they generate with the belief formation procedure. The framework allows sellers to have inconsistent and time-varying beliefs about each other. Under mild and natural assumptions on the APU, we show that despite the inconsistent and time-varying nature of beliefs, the market converges to a unique equilibrium at a linear rate (distance to equilibrium decreases exponentially in time). If the APU are driven by weak gross substitutes demands, the equilibrium point is the same as predicted by those demands.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.geb.2020.11.005DOIArticle
https://resolver.caltech.edu/CaltechAUTHORS:20170214-145943460Related ItemConference Paper
ORCID:
AuthorORCID
Dvijotham, Krishnamurthy0000-0002-1328-4677
Rabani, Yuval0000-0001-7772-2544
Schulman, Leonard J.0000-0001-9901-2797
Additional Information:© 2020 Elsevier Inc. Received 18 October 2018, Available online 14 December 2020. KD was supported by a fellowship from the Caltech Center for the Mathematics of Information. YR was supported in part by ISF grant 956-15, BSF grant 2012333 and I-CORE Algo. LJS was supported in part by NSF grants 1319745, 1618795, 1909972, and BSF grant 2012333. An earlier version of this paper appeared in Proc. 28th SODA, 2017.
Funders:
Funding AgencyGrant Number
Caltech Center for Mathematics of InformationUNSPECIFIED
Israel Science Foundation956-15
Binational Science Foundation (USA-Israel)2012333
I-CORE Program of the Planning and Budgeting CommitteeUNSPECIFIED
NSFCCF-1319745
NSFCCF-1618795
NSFCCF-1909972
Subject Keywords:Fisher markets; Disequilibrium; Market dynamics; Bounded rationality; Best response; Level k model
DOI:10.1016/j.geb.2020.11.005
Record Number:CaltechAUTHORS:20201217-133744650
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20201217-133744650
Official Citation:Krishnamurthy Dvijotham, Yuval Rabani, Leonard J. Schulman, Convergence of incentive-driven dynamics in Fisher markets, Games and Economic Behavior, Volume 134, 2022, Pages 361-375, ISSN 0899-8256, https://doi.org/10.1016/j.geb.2020.11.005. (https://www.sciencedirect.com/science/article/pii/S0899825620301585)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:107163
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:17 Dec 2020 22:22
Last Modified:11 Jul 2022 22:33

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