Dvijotham, Krishnamurthy and Rabani, Yuval and Schulman, Leonard J. (2020) Convergence of incentive-driven dynamics in Fisher markets. Games and Economic Behavior . ISSN 0899-8256. doi:10.1016/j.geb.2020.11.005. (In Press) 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.
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Additional Information: | © 2020 Elsevier. 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. | ||||||||||||||||
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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, 2020, , ISSN 0899-8256, https://doi.org/10.1016/j.geb.2020.11.005. | ||||||||||||||||
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: | 16 Nov 2021 19:00 |
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