Some Properties of a Decentralized Adjustment Process

This paper deals with some properties of a decentralized adjustment process which were investigated originally by T. A. Marschak in [Marschak, J. 1968. Computation in organizations: Comparison of price mechanisms and other adjustment processes. Risk and Uncertainty Proceedings of an International Economic Association Conference, Ch. XII. of McGuire, C. B., R. Radner (1972), eds. Borch and Mossin, St. Martin's Press, New York, 1972.]. We correct some mathematical errors. Marschak compares the gross expected payoffs of centralized and decentralized mechanisms. We prove that his Proposition 5: "the greater regular rate is the better" [Marschak, J. 1968. Computation in organizations: Comparison of price mechanisms and other adjustment processes. Risk and Uncertainty Proceedings of an International Economic Association Conference, Ch. XII. of McGuire, C. B., R. Radner (1972), eds. Borch and Mossin, St. Martin's Press, New York, 1972, p. 261] is not correct in this generality and replace it with the exact theorem on the rate-optimum. We analyse Marschak's Paradox 1 [Marschak, J. 1968. Computation in organizations: Comparison of price mechanisms and other adjustment processes. Risk and Uncertainty Proceedings of an International Economic Association Conference, Ch. XII. of McGuire, C. B., R. Radner (1972), eds. Borch and Mossin, St. Martin's Press, New York, 1972, p. 263: Proposition 6] and prove that it is not a real paradox, namely, that it would hold only if the components of a certain random variable-vector were correlated, a case treated separately. Finally Marschak's problem on the finiteness of a modified adjustment process is solved.