An impossibility theorem for price-adjustment mechanisms

作者:Papadimitriou Christos H*; Yannakakis Mihalis
来源:Proceedings of the National Academy of Sciences of the United States of America, 2010, 107(5): 1854-1859.
DOI:10.1073/pnas.0914728107

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 1/epsilon. 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.

  • 出版日期2010-2-2