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.
Research supported by NSF Grants ITR-0081698 and ITR-0121555, an IBM faculty development award, a Grant from RGC of HK SAR, China (CityU1081/02E) and a Grant of City University of Hong Kong (7001215).
