Uncomputability and Undecidability in Economic Theory
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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Date of creation:  2008 
Date of revision:  
Handle:  RePEc:trn:utwpde:0806 
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 Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979, December.
 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.
 K. Vela Velupillai, 2012. "Taming The Incomputable, Reconstructing The Nonconstructive And Deciding The Undecidable In Mathematical Economics," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 551.
 K. Vela Velupillai, 2007. "Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics," Department of Economics Working Papers 0722, Department of Economics, University of Trento, Italia.
 K. Vela Velupillai, 2004.
"The unreasonable ineffectiveness of mathematics in economics,"
Department of Economics Working Papers
0406, Department of Economics, University of Trento, Italia.
 K. Vela Velupillai, 2005. "The unreasonable ineffectiveness of mathematics in economics," Cambridge Journal of Economics, Oxford University Press, vol. 29(6), pages 849872, November.
 K. Vela Velupillai, 2004. "The Unreasonable Ineffectiveness of Mathematics in Economics," Working Papers 0080, National University of Ireland Galway, Department of Economics, revised 2004.
 K. Vela Velupillai, 2005.
"The Foundations of Computable General EquilibriumTheory,"
Working Papers
0093, National University of Ireland Galway, Department of Economics, revised 2005.
 K. Vela Velupillai, 2005. "The foundations of computable general equilibrium theory," Department of Economics Working Papers 0513, Department of Economics, University of Trento, Italia.
 (Vela) Velupillai, K., 1997. "Expository notes on computability and complexity in (arithmetical) games," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 955979, June.
 K. Vela Velupillai, 2007. "A Computable Economistâ€™s Perspective on Computational Complexity," Department of Economics Working Papers 0723, Department of Economics, University of Trento, Italia.
 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 S38599, October.
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