A Lower Bound on Computational Complexity Given by Revelation Mechanisms
AbstractThis 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 proves 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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Bibliographic InfoArticle provided by Springer in its journal Economic Theory.
Volume (Year): 7 (1996)
Issue (Month): 2 (February)
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Web page: http://link.springer.de/link/service/journals/00199/index.htm
Other versions of this item:
- Kenneth R. Mount & Stanley Reiter, 1996. "A lower bound on computational complexity given by revelation mechanisms (*)," Economic Theory, Springer, vol. 7(2), pages 237-266.
- 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.
- 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, Technological Change, and Growth - - Economic Development - - - Macroeconomic Analyses of Economic Development
- O47 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Measurement of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
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