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A Lower Bound on Computational Complexity Given by Revelation Mechanisms

  • Kenneth R. Mount
  • Stanley Reiter

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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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1085.pdf
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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
Contact details of provider: Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
Web page: http://www.kellogg.northwestern.edu/research/math/
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  1. 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.
  2. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
  3. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  4. Kenneth Mount & Stanley Reiter, 1973. "The Informational Size of Message Spaces," Discussion Papers 3, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  5. Jordan, J. S., 1982. "The competitive allocation process is informationally efficient uniquely," Journal of Economic Theory, Elsevier, vol. 28(1), pages 1-18, October.
  6. Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-92, May.
  7. 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.
  8. Reichelstein, Stefan, 1984. "Incentive compatibility and informational requirements," Journal of Economic Theory, Elsevier, vol. 34(1), pages 32-51, October.
  9. 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.
  10. Sonnenschein, Hugo, 1974. "An Axiomatic Characterization of the Price Mechanism," Econometrica, Econometric Society, vol. 42(3), pages 425-33, May.
  11. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
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