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Non-computability of competitive equilibrium

Author

Listed:
  • Kam-Chau Wong

    (Department of Economics, Chinese University of Hong Kong, Shatin, HONG KONG)

  • Marcel K. Richter

    (Department of Economics, University of Minnesota, Minneapolis, MN 55455, USA)

Abstract

We provide a "computable counterexample" to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a "computable counterexample" to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]).

Suggested Citation

  • Kam-Chau Wong & Marcel K. Richter, 1999. "Non-computability of competitive equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 1-27.
  • Handle: RePEc:spr:joecth:v:14:y:1999:i:1:p:1-27
    Note: Received: September 9, 1997; revised version: December 17, 1997
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    Citations

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    Cited by:

    1. Prasad, Kislaya, 2009. "The rationality/computability trade-off in finite games," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 17-26, January.
    2. Tolentino, P. E., 2004. "Computable Economics: the Arne Ryde Memorial Lecture Series: Kumaraswamy Velupillai (Ed.), Oxford University Press, Oxford, Vol. xiii, 2000, 222 pp., Index," Journal of Economic Behavior & Organization, Elsevier, vol. 54(3), pages 445-449, July.
    3. Miyake, Mitsunobu, 2003. "Precise computation of a competitive equilibrium of the discrete land market model," Regional Science and Urban Economics, Elsevier, vol. 33(6), pages 721-743, October.
    4. Edoardo Gaffeo & Domenico Delli Gatti & Saul Desiderio & Mauro Gallegati, 2008. "Adaptive Microfoundations for Emergent Macroeconomics," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 34(4), pages 441-463.
    5. Kumabe, Masahiro & Mihara, H. Reiju, 2008. "Computability of simple games: A characterization and application to the core," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 348-366, February.
    6. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    7. Rodrigo Jardim Raad, 2016. "Recursive equilibrium with Price Perfect Foresight and a minimal state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 1-54, January.
    8. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    9. Gaffeo, E. & Catalano, M. & Clementi, F. & Delli Gatti, D. & Gallegati, M. & Russo, A., 2007. "Reflections on modern macroeconomics: Can we travel along a safer road?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 89-97.
    10. Felix Kubler & Karl Schmedders, 2003. "Approximate Versus Exact Equilibria," Discussion Papers 1382, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Richard Holt & J. Barkley Rosser & David Colander, 2011. "The Complexity Era in Economics," Review of Political Economy, Taylor & Francis Journals, vol. 23(3), pages 357-369.
    12. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    13. J. Barkley Rosser Jr & Richard P.F. Holt & David Colander, 2010. "European Economics at a Crossroads," Books, Edward Elgar Publishing, number 13585.
    14. Barbara Dluhosch, 2011. "European Economics at a Crossroads, by J. Barkley Rosser, Jr., Richard P. F. Holt, and David Colander," Journal of Regional Science, Wiley Blackwell, vol. 51(3), pages 629-631, August.
    15. Potgieter, Petrus H. & Rosinger, Elemér E., 2007. "Is Economics Entering its Post-Witchcraft Era?," MPRA Paper 3340, University Library of Munich, Germany.

    More about this item

    Keywords

    Bounded rationality; Computability; General equilibrium; Recursive analysis.;

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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