A Simple Approximation Algorithm for Computing Arrow-Debreu Prices

Authors:
Mehdi Ghiyasvand;James B. Orlin
Affiliations:
Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran;Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Venue:
Operations Research
Year:
2012

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Abstract

We consider the Arrow-Debreu market with linear utilities in which there is a set G of divisible goods and a set B of buyers. Each buyer starts with an initial endowment of goods. The buyer's utility function is a linearly separable function of the goods that the buyer purchases. We develop a simple and efficient algorithm for determining an approximate market equilibrium. Our algorithm finds an ε-approximate solution in On/ε|B||G| time, where n = |B| + |G|. The running time can be further improved to On/εm + |B|log|B| where m is the number of pairs i, j such that buyer i has some utility for purchasing good j.