On the complexity of price equilibria

Authors:
Xiaotie Deng;Christos Papadimitriou;Shmuel Safra
Affiliations:
Department of Computer Science, City University of Hong Kong, Hong Kong SAR, China;Division of Computer Science, University of California, Berkeley, CA;School of Mathematical Sciences, Tel Aviv University, Israel
Venue:
Journal of Computer and System Sciences - STOC 2002
Year:
2003

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Abstract

We prove complexity, approximability, and inapproximability results for the problem of finding an exchange equilibrium in markets with indivisible (integer) goods, most notably a polynomial algorithm that approximates the market equilibrium arbitrarily close when the number of goods is bounded and the utilities linear. We also show a communication complexity lower bound in a model appropriate for markets. Our result implies that the ideal informational economy of a market with divisible goods and unique optimal allocations is unattainable in general.