# Uncomputability and Undecidability in Economic Theory

## Abstract

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.## Download Info

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## Bibliographic Info

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

**Length:**

**Date of creation:**2008

**Date of revision:**

**Handle:**RePEc:trn:utwpde:0806

**Contact details of provider:**

Postal: Via Inama 5, 38100 Trento

Phone: +39-461-882201

Fax: +39-461-882222

Web page: http://www.unitn.it/deco

More information through EDIRC

## Related research

**Keywords:**General Equilibrium Theory; Game Theory; Recursive Macro-economics; (Un)computability; (Un)decidability; Constructivity;

**Find related papers by JEL classification:**

**C60**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General**C63**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques**C68**- Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models**C70**- Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General**C79**- Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other

**This paper has been announced in the following NEP Reports:**

- NEP-ALL-2008-06-21 (All new papers)
- NEP-HPE-2008-06-21 (History & Philosophy of Economics)

## References

**References listed on IDEAS**

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.:

- K. Vela Velupillai, 2005.
"
**The unreasonable ineffectiveness of mathematics in economics**," Cambridge Journal of Economics, Oxford University Press, vol. 29(6), pages 849-872, 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, 2004.
"
**The unreasonable ineffectiveness of mathematics in economics**," Department of Economics Working Papers 0406, Department of Economics, University of Trento, Italia.

- K. Vela Velupillai, 2004.
"
- Marimon, Ramon & Scott, Andrew (ed.), 1999.
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**Computational Methods for the Study of Dynamic Economies**," OUP Catalogue, Oxford University Press, number 9780198294979, Octomber. - 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, 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 5-51.

- 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.
"
- 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.

- K. Vela Velupillai, 2005.
"
- 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. - (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. - 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.

**Full references**(including those not matched with items on IDEAS)

## Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.**Cited by:**

- K.Vela Velupillai, 2011.
"
**Negishi's Theorem and Method**," ASSRU Discussion Papers 1129, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2012.
"
**The Chimera of a Complete Analysis of Economic Dynamics**," ASSRU Discussion Papers 1207, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2011.
"
**DSGE And Beyond â€“ Computable And Constructive Challenges**," ASSRU Discussion Papers 1122, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2011.
"
**The Fundamental Theorems of Welfare Economics, DSGE and the Theory of Policy - Computable & Constructive Foundations**," ASSRU Discussion Papers 1125, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2012.
"
**"Dear Professor Mankiw..."- Reflections on Four Decades of Learning and Teaching Macroeconomics**," ASSRU Discussion Papers 1206, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2011.
"
**Foley's Thesis, Negishi's Method, Existence Proofs and Computation**," ASSRU Discussion Papers 1124, ASSRU - Algorithmic Social Science Research Unit.

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