Fast-converging tatonnement algorithms for one-time and ongoing market problems

Richard Cole, Lisa Fleischer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Why might markets tend toward and remain near equilibrium prices? In an effort to shed light on this question from an algorithmic perspective, this paper formalizes the setting of Ongoing Markets, by contrast with the classic market scenario, which we term One-Time Markets. The Ongoing Market allows trade at non-equilibrium prices, and, as its name suggests, continues over time. As such, it appears to be a more plausible model of actual markets. For both market settings, this paper defines and analyzes variants of a simple tatonnement algorithm that differs from previous algorithms that have been subject to asymptotic analysis in three significant respects: the price update for a good depends only on the price, demand, and supply for that good, and on no other information; the price update for each good occurs distributively and asynchronously; the algorithms work (and the analyses hold) from an arbitrary starting point. Our algorithm introduces a new and natural update rule. We show that this update rule leads to fast convergence toward equilibrium prices in a broad class of markets that satisfy the weak gross substitutes property. These are the first analyses for computationally and informationally distributed algorithms that demonstrate polynomial convergence. Our analysis identifies three parameters characterizing the markets, which govern the rate of convergence of our protocols. These parameters are, broadly speaking: 1. A bound on the fractional rate of change of demand for each good with respect to fractional changes in its price. 2. A bound on the fractional rate of change of demand for each good with respect to fractional changes in wealth. 3. The closeness of the market to a Fisher market (a market with buyers starting with money alone). We give two types of protocols. The first type assumes global knowledge of only (an upper bound on) the first parameter. For this protocol, we also provide a matching lower bound in terms of these parameters for the One-Time Market. Our second protocol, which is analyzed for the One-Time Market only, assumes no global knowledge whatsoever.

Original languageEnglish (US)
Title of host publicationSTOC'08
Subtitle of host publicationProceedings of the 2008 ACM Symposium on Theory of Computing
PublisherAssociation for Computing Machinery (ACM)
Pages315-324
Number of pages10
ISBN (Print)9781605580470
DOIs
StatePublished - 2008
Event40th Annual ACM Symposium on Theory of Computing, STOC 2008 - Victoria, BC, Canada
Duration: May 17 2008May 20 2008

Publication series

NameProceedings of the Annual ACM Symposium on Theory of Computing
ISSN (Print)0737-8017

Other

Other40th Annual ACM Symposium on Theory of Computing, STOC 2008
CountryCanada
CityVictoria, BC
Period5/17/085/20/08

Keywords

  • Market equilibria
  • Tatonnement

ASJC Scopus subject areas

  • Software

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  • Cite this

    Cole, R., & Fleischer, L. (2008). Fast-converging tatonnement algorithms for one-time and ongoing market problems. In STOC'08: Proceedings of the 2008 ACM Symposium on Theory of Computing (pp. 315-324). (Proceedings of the Annual ACM Symposium on Theory of Computing). Association for Computing Machinery (ACM). https://doi.org/10.1145/1374376.1374422