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Quantum Mechanics and Mathematical Economics are Isomorphic. John von Neumann between Physics and Economics

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  • L. Lambertini

Abstract

A methodological discussion is proposed, aiming at showing that game theory in particular (and mathematical economics in general) and quantum mechanics are isomorphic. This result 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. This coincidence can be traced back to the contributions of von Neumann in both disciplines.

Suggested Citation

  • 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.
    • Handle: RePEc:bol:bodewp:370
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    References listed on IDEAS

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    1. R. Myerson, 2010. "Nash Equilibrium and the History of Economic Theory," Voprosy Ekonomiki, NP Voprosy Ekonomiki, issue 6.
    2. van Damme, Eric, 1995. "On the Contributions of John C. Harsanyi, John F. Nash and Reinhard Selten," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 3-11.
    3. 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.
    4. repec:bla:scandj:v:97:y:1995:i:1:p:15-40 is not listed on IDEAS
    5. 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.
    6. Peter Fishburn & Peter Wakker, 1995. "The Invention of the Independence Condition for Preferences," Management Science, INFORMS, vol. 41(7), pages 1130-1144, July.
    7. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    8. 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.
    9. 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.
    10. 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.
    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. van Damme, E.E.C. & Weibull, J.W., 1995. "Equilibrium in strategic interaction : The contributions of John C. Harsanyi, John F. Nash and Reinhard Selten," Other publications TiSEM de9d99b7-7e74-4c92-90fc-b, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Dino Borie, 2013. "Expected utility theory with non-commutative probability theory," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(2), pages 295-315, October.
    2. Mukhopadhyay, Archan & Sur, Saikat & Saha, Tanay & Sadhukhan, Shubhadeep & Chakraborty, Sagar, 2024. "Repeated quantum game as a stochastic game: Effects of the shadow of the future and entanglement," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    3. Edward W. Piotrowski & Jan Sladkowski, "undated". "Trading by Quantum Rules - Quantum Anthropic Principle," Departmental Working Papers 9, University of Bialtystok, Department of Theoretical Physics.

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