期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2010
卷号：107
期号：5
页码：1854-1859
DOI：10.1073/pnas.0914728107
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：We show that there is no discrete-time price-adjustment mechanism (any process that at each period looks at the history of prices and excess demands and updates the prices) such that for any market (a set of goods and consumers with endowments and strictly concave utilities) the price-adjustment mechanism will achieve excess demands that are at most an{epsilon} fraction of the total supply within a number of periods that is polynomial in the number of goods and [IMG]/medium/pnas.0914728107eq1.gif" ALT="Formula ">. This holds even if one restricts markets so that excess demand functions are differentiable with derivatives bounded by a small constant. For the convergence time to the actual price equilibrium, we show by a different method a stronger result: Even in the case of three goods with a unique price equilibrium, there is no function of{epsilon} that bounds the number of periods needed by a price-adjustment mechanism to arrive at a set of prices that is{epsilon} -close to the equilibrium.
关键词：Arrow–Debreu theorem ; complexity ; fixed point ; price equilibrium
