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Can Markets Compute Equilibria?

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  • Hunter K. Monroe
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    Abstract

    Recent turmoil in financial and commodities markets has renewed questions regarding how well markets discover equilibrium prices, particularly when those markets are highly complex. A relatively new critique questions whether markets can realistically find equilibrium prices if computers cannot. For instance, in a simple exchange economy with Leontief preferences, the time required to compute equilibrium prices using the fastest known techniques is an exponential function of the number of goods. Furthermore, no efficient technique for this problem exists if a famous mathematical conjecture is correct. The conjecture states loosely that there are some problems for which finding an answer (i.e., an equilibrium price vector) is hard even though it is easy to check an answer (i.e., that a given price vector is an equilibrium). This paper provides a brief overview of computational complexity accessible to economists, and points out that the existence of computational problems with no best solution algorithm is relevant to this conjecture.

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    Bibliographic Info

    Paper provided by International Monetary Fund in its series IMF Working Papers with number 09/24.

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    Length: 22
    Date of creation: 01 Feb 2009
    Date of revision:
    Handle: RePEc:imf:imfwpa:09/24

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    Related research

    Keywords: Commodity markets; Prices; Economic models; problems; polynomial; computational complexity; arithmetic; computation; mathematics; equation; complexity theory; probability; mathematicians; computations; linear time; applied mathematics; survey; function log; probability distribution; combinatorics; minimization;

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    1. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, Elsevier, vol. 1(1), pages 80-93, March.
    2. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, Elsevier, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
    3. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, SUNY-Oswego, Department of Economics, number comp1, Spring.
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