IDEAS home Printed from https://ideas.repec.org/p/rim/rimwps/40_13.html
   My bibliography  Save this paper

John von Neumann between Physics and Economics: A Methodological Note

Author

Listed:
  • Luca Lambertini

    (Department of Economics, University of Bologna, Italy)

Abstract

A methodological discussion is proposed, aiming at illustrating an analogy between game theory in particular (and mathematical economics in general) and quantum mechanics. This analogy relies on the equivalence of the two fundamental operators employed in the two fields, namely, the expected value in economics and the density matrix in quantum physics. I conjecture that this coincidence can be traced back to the contributions of von Neumann in both disciplines.

Suggested Citation

  • Luca Lambertini, 2013. "John von Neumann between Physics and Economics: A Methodological Note," Working Paper series 40_13, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:40_13
    as

    Download full text from publisher

    File URL: http://www.rcea.org/RePEc/pdf/wp40_13.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Piotrowski, E.W & Sładkowski, J, 2002. "Quantum market games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(1), pages 208-216.
    2. Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
    3. Mirowski,Philip, 2002. "Machine Dreams," Cambridge Books, Cambridge University Press, number 9780521772839, September.
    4. Robert J. Leonard, 1995. "From Parlor Games to Social Science: Von Neumann, Morgenstern, and the Creation of Game Theory, 1928-1994," Journal of Economic Literature, American Economic Association, vol. 33(2), pages 730-761, June.
    5. Richard Mckelvey & Thomas Palfrey, 1998. "Quantal Response Equilibria for Extensive Form Games," Experimental Economics, Springer;Economic Science Association, vol. 1(1), pages 9-41, June.
    6. Mirowski,Philip, 2002. "Machine Dreams," Cambridge Books, Cambridge University Press, number 9780521775267, September.
    7. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    8. Walker, D A, 1991. "Economics as Social Physics: Review Article," Economic Journal, Royal Economic Society, vol. 101(406), pages 615-631, May.
    9. Peter Fishburn & Peter Wakker, 1995. "The Invention of the Independence Condition for Preferences," Management Science, INFORMS, vol. 41(7), pages 1130-1144, July.
    10. Paul Klemperer & Margaret Meyer, 1986. "Price Competition vs. Quantity Competition: The Role of Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 17(4), pages 618-638, Winter.
    11. Leland, Hayne E, 1972. "Theory of the Firm Facing Uncertain Demand," American Economic Review, American Economic Association, vol. 62(3), pages 278-291, June.
    12. Edward W. Piotrowski & Jan Sladkowski, "undated". "Trading by Quantum Rules - Quantum Anthropic Principle," Departmental Working Papers 9, University of Bialtystok, Department of Theoretical Physics.
    13. R. Myerson, 2010. "Nash Equilibrium and the History of Economic Theory," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 6.
    14. Robert J. Leonard, 1992. "Reading Cournot, Reading Nash / or / The Emergence and Stabilization of the Nash equilibrium," Cahiers de recherche du Département des sciences économiques, UQAM 9214, Université du Québec à Montréal, Département des sciences économiques.
    15. Leonard,Robert, 2010. "Von Neumann, Morgenstern, and the Creation of Game Theory," Cambridge Books, Cambridge University Press, number 9780521562669, September.
    16. Richard D. Mckelvey & Thomas R. Palfrey, 1996. "A Statistical Theory Of Equilibrium In Games," The Japanese Economic Review, Japanese Economic Association, vol. 47(2), pages 186-209, June.
    17. Edward W. Piotrowski & Jan Sladkowski, "undated". "An Invitation to Quantum Game Theory," Departmental Working Papers 15, University of Bialtystok, Department of Theoretical Physics.
    18. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    19. Philip Mirowski, 1992. "What Were von Neumann and Morgenstern Trying to Accomplish?," History of Political Economy, Duke University Press, vol. 24(5), pages 113-147, Supplemen.
    20. Leonard, Robert J, 1994. "Reading Cournot, Reading Nash: The Creation and Stabilisation of the Nash Equilibrium," Economic Journal, Royal Economic Society, vol. 104(424), pages 492-511, May.
    21. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    22. Siegfried G. Karsten, 1990. "Quantum Theory and Social Economics:," American Journal of Economics and Sociology, Wiley Blackwell, vol. 49(4), pages 385-399, October.
    23. Edward W. Piotrowski & Jan Sladkowski, "undated". "The Next Stage: Quantum Game Theory," Departmental Working Papers 18, University of Bialtystok, Department of Theoretical Physics.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. L. Lambertini, 2000. "Quantum Mechanics and Mathematical Economics are Isomorphic. John von Neumann between Physics and Economics," Working Papers 370, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Jorge Streb, 2010. "Hume: The power of abduction and simple observation in economics," CEMA Working Papers: Serie Documentos de Trabajo. 417, Universidad del CEMA.
    3. Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantum Games and Programmable Quantum Systems," Departmental Working Papers 22, University of Bialtystok, Department of Theoretical Physics.
    4. Turan Yay & Huseyin Tastan, 2010. "Invisible Hand in the Process of Making Economics or on the Method and Scope of Economics," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 57(1), pages 61-83, March.
    5. Katarzyna Miakisz & Edward W. Piotrowski & Jan Sladkowski, "undated". "Quantization of Games: Towards Quantum Artificial Intelligence," Departmental Working Papers 21, University of Bialtystok, Department of Theoretical Physics.
    6. Choo, Lawrence C.Y & Kaplan, Todd R., 2014. "Explaining Behavior in the "11-20" Game," MPRA Paper 52808, University Library of Munich, Germany.
    7. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.
    8. Yi, Kang-Oh, 2005. "Quantal-response equilibrium models of the ultimatum bargaining game," Games and Economic Behavior, Elsevier, vol. 51(2), pages 324-348, May.
    9. Emmanuel Haven, 2008. "Private Information and the ‘Information Function’: A Survey of Possible Uses," Theory and Decision, Springer, vol. 64(2), pages 193-228, March.
    10. Brown, Murray & Chiang, Shin-Hwan, 2002. "Unsystematic risk and coalition formation in product markets," International Journal of Industrial Organization, Elsevier, vol. 20(3), pages 313-338, March.
    11. Casella, Alessandra & Gelman, Andrew & Palfrey, Thomas R., 2006. "An experimental study of storable votes," Games and Economic Behavior, Elsevier, vol. 57(1), pages 123-154, October.
    12. James W. Friedman, 2000. "The legacy of Augustin Cournot," Cahiers d'Économie Politique, Programme National Persée, vol. 37(1), pages 31-46.
    13. Edward W. Piotrowski, "undated". "Quantum Mind. A sketch (in Polish)," Departmental Working Papers 120pl, University of Bialtystok, Department of Theoretical Physics.
    14. Gailmard, Sean & Palfrey, Thomas R., 2005. "An experimental comparison of collective choice procedures for excludable public goods," Journal of Public Economics, Elsevier, vol. 89(8), pages 1361-1398, August.
    15. Piotrowski, Edward W. & Sładkowski, Jan, 2008. "Quantum auctions: Facts and myths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3949-3953.
    16. Juan D. Carrillo & Thomas R. Palfrey, 2009. "The Compromise Game: Two-Sided Adverse Selection in the Laboratory," American Economic Journal: Microeconomics, American Economic Association, vol. 1(1), pages 151-181, February.
    17. Alessandro Innocenti, 2004. "Paradoxes versus formalism in economics. Evidence from the early years of game theory and experimental economics," Department of Economics University of Siena 433, Department of Economics, University of Siena.
    18. Boris Salazar, 2004. "Nash y von Neumann: mundos posibles y juegos de lenguaje," Revista de Economía Institucional, Universidad Externado de Colombia - Facultad de Economía, vol. 6(10), pages 71-94, January-J.
    19. Jacob Goeree & Charles Holt & Thomas Palfrey, 2005. "Regular Quantal Response Equilibrium," Experimental Economics, Springer;Economic Science Association, vol. 8(4), pages 347-367, December.
    20. Costa-Gomes, Miguel & Zauner, Klaus G., 2001. "Ultimatum Bargaining Behavior in Israel, Japan, Slovenia, and the United States: A Social Utility Analysis," Games and Economic Behavior, Elsevier, vol. 34(2), pages 238-269, February.

    More about this item

    Keywords

    expected value; density matrix; uncertainty; quantum games;
    All these keywords.

    JEL classification:

    • B25 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Historical; Institutional; Evolutionary; Austrian; Stockholm School
    • B41 - Schools of Economic Thought and Methodology - - Economic Methodology - - - Economic Methodology
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:rim:rimwps:40_13. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Marco Savioli (email available below). General contact details of provider: https://edirc.repec.org/data/rcfeait.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.