A lower bound on computational complexity given by revelation mechanisms (*)
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 ) 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.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
Volume (Year): 7 (1996)
Issue (Month): 2 ()
|Contact details of provider:|| Web page: http://link.springer.de/link/service/journals/00199/index.htm|
|Order Information:||Web: http://link.springer.de/orders.htm|
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.:
- Saari, Donald G & Simon, Carl P, 1978. "Effective Price Mechanisms," Econometrica, Econometric Society, vol. 46(5), pages 1097-1125, September.
- Neyman, Abraham, 1985. "Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma," Economics Letters, Elsevier, vol. 19(3), pages 227-229.
- Reichelstein, Stefan & Reiter, Stanley, 1988. "Game Forms with Minimal Message Spaces," Econometrica, Econometric Society, vol. 56(3), pages 661-92, May.
- 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.
- 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.
- Reichelstein, Stefan, 1984. "Incentive compatibility and informational requirements," Journal of Economic Theory, Elsevier, vol. 34(1), pages 32-51, October.
- 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.
- Ehud Kalai & William Stanford, 1986.
"Finite Rationality and Interpersonal Complexity in Repeated Games,"
679, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
- Sonnenschein, Hugo, 1974. "An Axiomatic Characterization of the Price Mechanism," Econometrica, Econometric Society, vol. 42(3), pages 425-33, May.
- Mount, Kenneth & Reiter, Stanley, 1974.
"The informational size of message spaces,"
Journal of Economic Theory,
Elsevier, vol. 8(2), pages 161-192, June.
- Jordan, J. S., 1982. "The competitive allocation process is informationally efficient uniquely," Journal of Economic Theory, Elsevier, vol. 28(1), pages 1-18, October.
When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:7:y:1996:i:2:p:237-266. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn)or (Christopher F Baum)
If references are entirely missing, you can add them using this form.