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A Simple and Efficient Algorithm for Computing Market Equilibria

Published: 13 May 2016 Publication History

Abstract

We give a new mathematical formulation of market equilibria in exchange economies using an indirect utility function: the function of prices and income that gives the maximum utility achievable. The formulation is a convex program and can be solved when the indirect utility function is convex in prices. We illustrate that many economies, including:
—Homogeneous utilities of degree α ∈ [0, 1] in Fisher economies—this includes Linear, Leontief, Cobb-Douglas
Resource allocation utilities like multi-commodity flows
satisfy this condition and can be efficiently solved.
Further, we give a natural tâtonnement type price-adjusting algorithm in these economies. Our algorithm, which is applicable to a larger class of utility functions than previously known weak gross substitutes, mimics the natural dynamics for the markets as suggested by Walras: it iteratively adjusts a good’s price upward when the demand for that good under current prices exceeds its supply; and downward when its supply exceeds its demand. The algorithm computes an approximate equilibrium in a number of iterations that is independent of the number of traders and is almost linear in the number of goods.

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  • (2019)Ascending-Price Algorithms for Unknown MarketsACM Transactions on Algorithms10.1145/331939415:3(1-33)Online publication date: 7-Jun-2019

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cover image ACM Transactions on Algorithms
ACM Transactions on Algorithms  Volume 12, Issue 3
June 2016
408 pages
ISSN:1549-6325
EISSN:1549-6333
DOI:10.1145/2930058
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

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Publication History

Published: 13 May 2016
Accepted: 01 December 2015
Revised: 01 March 2015
Received: 01 March 2010
Published in TALG Volume 12, Issue 3

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  1. Market equilibrium
  2. approximation algorithms

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View all
  • (2022)Implementing Machine Learning for Supply-Demand Shifts and Price Impacts in Farmer Market for Tool and Equipment SharingJournal of Food Quality10.1155/2022/44964492022(1-19)Online publication date: 15-Mar-2022
  • (2019)Ascending-Price Algorithms for Unknown MarketsACM Transactions on Algorithms10.1145/331939415:3(1-33)Online publication date: 7-Jun-2019

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