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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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    Cited by:

    1. 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.
    2. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    3. 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.
    4. 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.
    5. 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.
    6. Rodrigo 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.
    7. Felix Kubler & Karl Schmedders, 2003. "Approximate Versus Exact Equilibria," Discussion Papers 1382, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Glaciel, William, 2020. "On non-computability of dynamic stochastic general equilibrium," OSF Preprints 23ep9, Center for Open Science.
    9. 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.
    10. Bell, William Paul, 2009. "Adaptive interactive expectations: dynamically modelling profit expectations," MPRA Paper 38260, University Library of Munich, Germany, revised 09 Feb 2010.
    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. Dargaj, Jakub & Simonsen, Jakob Grue, 2023. "A complete characterization of infinitely repeated two-player games having computable strategies with no computable best response under limit-of-means payoff," Journal of Economic Theory, Elsevier, vol. 213(C).
    13. Roberto Cazzolla Gatti & Roger Koppl & Brian D. Fath & Stuart Kauffman & Wim Hordijk & Robert E. Ulanowicz, 2020. "On the emergence of ecological and economic niches," Journal of Bioeconomics, Springer, vol. 22(2), pages 99-127, July.
    14. Icefield, William, 2020. "Nature and Logic," OSF Preprints btg7q, Center for Open Science.
    15. Prasad, Kislaya, 2009. "The rationality/computability trade-off in finite games," Journal of Economic Behavior & Organization, Elsevier, vol. 69(1), pages 17-26, January.
    16. 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.
    17. Jakub Dargaj & Jakob Grue Simonsen, 2020. "A Complete Characterization of Infinitely Repeated Two-Player Games having Computable Strategies with no Computable Best Response under Limit-of-Means Payoff," Papers 2005.13921, arXiv.org, revised Jun 2020.
    18. Jiun-Hua Su, 2019. "Model Selection in Utility-Maximizing Binary Prediction," Papers 1903.00716, arXiv.org, revised Jul 2020.
    19. Simone Landini & Mauro Gallegati & J. Barkley Rosser, 2020. "Consistency and incompleteness in general equilibrium theory," Journal of Evolutionary Economics, Springer, vol. 30(1), pages 205-230, January.
    20. J. Barkley Rosser Jr & Richard P.F. Holt & David Colander, 2010. "European Economics at a Crossroads," Books, Edward Elgar Publishing, number 13585.
    21. 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.
    22. Potgieter, Petrus H. & Rosinger, Elemér E., 2007. "Is Economics Entering its Post-Witchcraft Era?," MPRA Paper 3340, University Library of Munich, Germany.
    23. Icefield, William, 2020. "On Marshallian theory of demand and short-run equilibrium," OSF Preprints 5du4z, Center for Open Science.
    24. Su, Jiun-Hua, 2021. "Model selection in utility-maximizing binary prediction," Journal of Econometrics, Elsevier, vol. 223(1), pages 96-124.
    25. 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.

    More about this item

    Keywords

    Bounded rationality; Computability; General equilibrium; Recursive analysis.;
    All these keywords.

    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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