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A lower bound on computational complexity given by revelation mechanisms (*)

  • Kenneth R. Mount
  • Stanley Reiter

This paper establishes a lower bound on the computational complexity of smooth functions between smooth manifolds. It generalizes one for finite (Boolean) functions obtained (by Arbib and Spira [2]) by counting variables. Instead of a counting procedure, which cannot be used in the infinite case, the dimension of the message space of a certain type of revelation mechanism provides the bound. It also provides an intrinsic measure of the number of variables on which the function depends. This measure also gives a lower bound on computational costs associated with realizing or implementing the function by a decentralized mechanism, or by a game form.

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 7 (1996)
Issue (Month): 2 ()
Pages: 237-266

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Handle: RePEc:spr:joecth:v:7:y:1996:i:2:p:237-266
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  1. Ehud Kalai & William Stanford, 1986. "Finite Rationality and Interpersonal Complexity in Repeated Games," Discussion Papers 679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Sonnenschein, Hugo, 1974. "An Axiomatic Characterization of the Price Mechanism," Econometrica, Econometric Society, vol. 42(3), pages 425-33, May.
  3. 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.
  4. 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.
  5. Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
  6. Mount, Kenneth & Reiter, Stanley, 1974. "The informational size of message spaces," Journal of Economic Theory, Elsevier, vol. 8(2), pages 161-192, June.
  7. Reichelstein, Stefan, 1984. "Incentive compatibility and informational requirements," Journal of Economic Theory, Elsevier, vol. 34(1), pages 32-51, October.
  8. Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-92, May.
  9. Jordan, J. S., 1982. "The competitive allocation process is informationally efficient uniquely," Journal of Economic Theory, Elsevier, vol. 28(1), pages 1-18, October.
  10. Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
  11. 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.
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