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Computability and Algorithmic Complexity in Economics

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  • K. Vela Velupillai
  • Stefano Zambelli

Abstract

This is an outline of the origins and development of the way computability theory and algorithmic complexity theory were incorporated into economic and finance theories. We try to place, in the context of the development of computable economics, some of the classics of the subject as well as those that have, from time to time, been credited with having contributed to the advancement of the field. Speculative thoughts on where the frontiers of computable economics are, and how to move towards them, conclude the paper. In a precise sense - both historically and analytically - it would not be an exaggeration to claim that both the origins of computable economics and its frontiers are defined by two classics, both by Banach and Mazur: that one page masterpiece by Banach and Mazur ([5]), built on the foundations of Turing’s own classic, and the unpublished Mazur conjecture of 1928, and its unpublished proof by Banach ([38], ch. 6 & [68], ch. 1, #6). For the undisputed original classic of computable economics is Rabinís effectivization of the Gale-Stewart game ([42];[16]); the frontiers, as I see them, are defined by recursive analysis and constructive mathematics, underpinning computability over the computable and constructive reals and providing computable foundations for the economist’s Marshallian penchant for curve-sketching ([9]; [19]; and, in general, the contents of Theoretical Computer Science, Vol. 219, Issue 1-2). The former work has its roots in the Banach-Mazur game (cf. [38], especially p.30), at least in one reading of it; the latter in ([5]), as well as other, earlier, contributions, not least by Brouwer.

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Paper provided by ASSRU - Algorithmic Social Science Research Unit in its series ASSRU Discussion Papers with number 1202.

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Date of creation: 2012
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Handle: RePEc:trn:utwpas:1202

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  1. K. Vela Velupillai, 2011. "Freedom, Anarchy and Conformism in Academic Research," ASSRU Discussion Papers 1123, ASSRU - Algorithmic Social Science Research Unit.
  2. (Vela) Velupillai, K., 1997. "Expository notes on computability and complexity in (arithmetical) games," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 955-979, June.
  3. K. Vela Velupillai, 2012. "Reflections On Mathematical Economics In The Algorithmic Mode," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 139-152.
  4. K.Vela Velupillai, 2010. "Nonlinear Dynamics, Complexity and Randomness: Algorithmic Foundations," ASSRU Discussion Papers 1020, ASSRU - Algorithmic Social Science Research Unit.
  5. Velupillai, K., 2000. "Computable Economics: The Arne Ryde Memorial Lectures," OUP Catalogue, Oxford University Press, number 9780198295273, September.
  6. Kumaraswamy Velupillai, . "The Computable Approach to Economics," Working Papers _005, University of California at Los Angeles, Center for Computable Economics.
  7. Arrow, Kenneth J, 1986. "Rationality of Self and Others in an Economic System," The Journal of Business, University of Chicago Press, vol. 59(4), pages S385-99, October.
  8. K. Vela Velupillai, 2011. "Towards an Algorithmic Revolution in Economic Theory," ASSRU Discussion Papers 1105, ASSRU - Algorithmic Social Science Research Unit.
  9. Smale, Stephen, 1976. "Dynamics in General Equilibrium Theory," American Economic Review, American Economic Association, vol. 66(2), pages 288-94, May.
  10. Winter, Sidney G, 1986. "Comments [Rationality of Self and Others in an Economic System] [Adaptive Behavior and Economic Theory]," The Journal of Business, University of Chicago Press, vol. 59(4), pages S427-34, October.
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