# 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

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are**not**on the IDEAS site. Please be patient as the files may be large.

## 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, 2004.
"
**The Unreasonable Ineffectiveness of Mathematics in Economics**," Working Papers, National University of Ireland Galway, Department of Economics 0080, National University of Ireland Galway, Department of Economics, revised 2004.

- K. Vela Velupillai, 2005.
"
**The unreasonable ineffectiveness of mathematics in economics**," Cambridge Journal of Economics, Oxford University Press, Oxford University Press, vol. 29(6), pages 849-872, November.

- K. Vela Velupillai, 2004.
"
**The unreasonable ineffectiveness of mathematics in economics**," Department of Economics Working Papers, Department of Economics, University of Trento, Italia 0406, Department of Economics, University of Trento, Italia.

- K. Vela Velupillai, 2005.
"
- K. Vela Velupillai, 2007.
"
**A Computable Economistâ€™s Perspective on Computational Complexity**," Department of Economics Working Papers, Department of Economics, University of Trento, Italia 0723, Department of Economics, University of Trento, Italia. - K. Vela Velupillai, 2007.
"
**Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics**," Department of Economics Working Papers, Department of Economics, University of Trento, Italia 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., 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, National University of Ireland Galway, Department of Economics 0128, National University of Ireland Galway, Department of Economics, revised 2007.

- K. Vela Velupillai, 2012.
"
- Arrow, Kenneth J, 1986.
"
**Rationality of Self and Others in an Economic System**," The Journal of Business, University of Chicago Press, 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, Elsevier, vol. 21(6), pages 955-979, June. - K. Vela Velupillai, 2005.
"
**The foundations of computable general equilibrium theory**," Department of Economics Working Papers, Department of Economics, University of Trento, Italia 0513, Department of Economics, University of Trento, Italia.

- K. Vela Velupillai, 2005.
"
**The Foundations of Computable General EquilibriumTheory**," Working Papers, National University of Ireland Galway, Department of Economics 0093, National University of Ireland Galway, Department of Economics, revised 2005.

- K. Vela Velupillai, 2005.
"
- Marimon, Ramon & Scott, Andrew (ed.), 1999.
"
**Computational Methods for the Study of Dynamic Economies**," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198294979, October.

**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, ASSRU - Algorithmic Social Science Research Unit 1129, 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, ASSRU - Algorithmic Social Science Research Unit 1206, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2011.
"
**DSGE And Beyond â€“ Computable And Constructive Challenges**," ASSRU Discussion Papers, ASSRU - Algorithmic Social Science Research Unit 1122, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2011.
"
**Foley's Thesis, Negishi's Method, Existence Proofs and Computation**," ASSRU Discussion Papers, ASSRU - Algorithmic Social Science Research Unit 1124, ASSRU - Algorithmic Social Science Research Unit. - K. Vela Velupillai, 2012.
"
**The Chimera of a Complete Analysis of Economic Dynamics**," ASSRU Discussion Papers, ASSRU - Algorithmic Social Science Research Unit 1207, 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, ASSRU - Algorithmic Social Science Research Unit 1125, ASSRU - Algorithmic Social Science Research Unit.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.## Statistics

Access and download statistics## Corrections

When requesting a correction, please mention this item's handle: RePEc:trn:utwpde:0806. See general information about how to correct material in RePEc.For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Luciano Andreozzi).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.