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Uncomputability and Undecidability in Economic Theory

  • K. Vela Velupillai


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    Economic theory, game theory and mathematical statistics have all increasingly become algorithmic sciences. Computable Economics, Algorithmic Game Theory ([28]) and Algorithmic Statistics ([13]) are frontier research subjects. All of them, each in its own way, are underpinned by (classical) recursion theory - and its applied branches, say computational complexity theory or algorithmic information theory - and, occasionally, proof theory. These research paradigms have posed new mathematical and metamathematical questions and, inadvertently, undermined the traditional mathematical foundations of economic theory. A concise, but partial, pathway into these new frontiers is the subject matter of this paper. Interpreting the core of mathematical economic theory to be defined by General Equilibrium Theory and Game Theory, a general - but concise - analysis of the computable and decidable content of the implications of these two areas are discussed. Issues at the frontiers of macroeconomics, now dominated by Recursive Macroeconomic Theory, are also tackled, albeit ultra briefly. The point of view adopted is that of classical recursion theory and varieties of constructive mathematics.

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    Paper provided by Department of Economics, University of Trento, Italia in its series Department of Economics Working Papers with number 0806.

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    Date of creation: 2008
    Date of revision:
    Handle: RePEc:trn:utwpde:0806
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    1. K. Vela Velupillai, 2004. "The Unreasonable Ineffectiveness of Mathematics in Economics," Working Papers 0080, National University of Ireland Galway, Department of Economics, revised 2004.
    2. 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.
    3. K. Vela Velupillai, 2005. "The Foundations of Computable General EquilibriumTheory," Working Papers 0093, National University of Ireland Galway, Department of Economics, revised 2005.
    4. K. Vela Velupillai, 2007. "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics," Working Papers 0128, National University of Ireland Galway, Department of Economics, revised 2007.
    5. (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.
    6. K. Vela Velupillai, 2007. "A Computable Economist’s Perspective on Computational Complexity," Department of Economics Working Papers 0723, Department of Economics, University of Trento, Italia.
    7. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
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