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A Lower Bound on Computational Complexity Given by Revelation Mechanisms

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  • Kenneth R. Mount
  • Stanley Reiter

Abstract

This paper establishes an elementary lower bound on the computational complexity of smooth functions between Euclidean spaces(actually, smooth manifolds). The main motivation for this comes from mechanism design theory. The complexity of computations required by a mechanism determines an element of the costs associated with that mechanism. The lower bound presented in this paper is useful in part because it does not require specification in detail of the computations to be performed by the mechanism, but depends only on the goal function that the mechanism is to realize or implement.

Suggested Citation

  • Kenneth R. Mount & Stanley Reiter, 1994. "A Lower Bound on Computational Complexity Given by Revelation Mechanisms," Discussion Papers 1085, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1085
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    References listed on IDEAS

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    8. Chen, Pengyuan, 1992. "A lower bound for the dimension of the message space of the decentralized mechanisms realizing a given goal," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 249-270.
    9. Sonnenschein, Hugo, 1974. "An Axiomatic Characterization of the Price Mechanism," Econometrica, Econometric Society, vol. 42(3), pages 425-433, May.
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    Cited by:

    1. Van Zandt, Timothy, 2003. "Real-Time Hierarchical Resource Allocation with Quadratic Costs," CEPR Discussion Papers 4022, C.E.P.R. Discussion Papers.
    2. Ehud Kalai, 1995. "Games," Discussion Papers 1141, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Tierney, Ryan, 2021. "Simple Social Choice Rules for Exchange," Discussion Papers on Economics 4/2021, University of Southern Denmark, Department of Economics.
    4. Marschak, Thomas, 2006. "Organization Structure," MPRA Paper 81518, University Library of Munich, Germany.
    5. Mehmet Barlo & Nuh Aygün Dalkıran, 2022. "Computational implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 605-633, December.

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    More about this item

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • O11 - Economic Development, Innovation, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence

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