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A Lower Bound on Computational Complexity Given by Revelation Mechanisms

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Kenneth R. Mount
Stanley Reiter

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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.

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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1085.

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Date of creation: Mar 1994
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Handle: RePEc:nwu:cmsems:1085

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Sonnenschein, Hugo, 1974. "An Axiomatic Characterization of the Price Mechanism," Econometrica, Econometric Society, vol. 42(3), pages 425-33, May. [Downloadable!] (restricted)
  2. Reichelstein, Stefan, 1984. "Incentive compatibility and informational requirements," Journal of Economic Theory, Elsevier, vol. 34(1), pages 32-51, October. [Downloadable!] (restricted)
  3. Stefan Reichelstein, 1981. "On the Informational Requirements for the Implementation of Social Choice Rules," Discussion Papers 507, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. Mount, Kenneth & Reiter, Stanley, 1974. "The informational size of message spaces," Journal of Economic Theory, Elsevier, vol. 8(2), pages 161-192, June. [Downloadable!] (restricted)
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  6. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September. [Downloadable!] (restricted)
  7. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229. [Downloadable!] (restricted)
  8. Jordan, J. S., 1982. "The competitive allocation process is informationally efficient uniquely," Journal of Economic Theory, Elsevier, vol. 28(1), pages 1-18, October. [Downloadable!] (restricted)
  9. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March. [Downloadable!] (restricted)
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  10. Kenneth R. Mount & Stanley Reiter, 1983. "On the Existence of a Locally Stable Dynamic Process With a Statically Minimal Message Space," Discussion Papers 550, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Van Zandt, Timothy, 2003. "Real-Time Hierarchical Resource Allocation with Quadratic Costs," CEPR Discussion Papers 4022, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  2. Ehud Kalai, 1995. "Games," Discussion Papers 1141, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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