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Basic Framework for Games with Quantum-like Players

Author

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  • Ariane Lambert-Mogiliansky

    (PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

  • Ismael Martinez-Martinez

    (DUCE - Dusseldorf Institute for Competition Economics - Heinrich-Heine-Universität Düsseldorf [Düsseldorf])

Abstract

We develop a framework for the analysis of strategic interactions under the constructive preference perspective à la Kahneman and Tversky formalized in the Type Indeterminacy model. The players are modeled as systems subject to measurements and characterized by quantum-like uncertain preferences. The decision nodes are modeled as, possibly non-commuting, operators that measure preferences modulo strategic reasoning. We define a Hilbert space of types spanned by the players' eigentypes representing their potential preferences in different situations. We focus on pure strategy TI games of maximal information where all uncertainty stems from the intrinsic indeterminacy of preferences. We show that preferences evolve in a non-deterministic manner with actions along the play: they are endogenous to the interaction. We propose the notion of cashing-on-the-go to compute a player's utility, and the Type Indeterminate Nash Equilibrium as a solution concept relying on best-replies at the level of the eigentypes. We illustrate an example exhibiting the phenomenon of the manipulation of rivals' preferences.

Suggested Citation

  • Ariane Lambert-Mogiliansky & Ismael Martinez-Martinez, 2014. "Basic Framework for Games with Quantum-like Players," PSE Working Papers hal-01095472, HAL.
  • Handle: RePEc:hal:psewpa:hal-01095472
    Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/hal-01095472
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    References listed on IDEAS

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    1. Ferreira J. -L. & Gilboa I. & Maschler M., 1995. "Credible Equilibria in Games with Utilities Changing during the Play," Games and Economic Behavior, Elsevier, vol. 10(2), pages 284-317, August.
    2. Danilov, V.I. & Lambert-Mogiliansky, A., 2008. "Measurable systems and behavioral sciences," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 315-340, May.
    3. Pierfrancesco La Mura, 2003. "Correlated Equilibria of Classical Strategic Games with Quantum Signals," Game Theory and Information 0309001, University Library of Munich, Germany.
    4. Loewenstein, George, 2008. "Exotic Preferences: Behavioral Economics and Human Motivation," OUP Catalogue, Oxford University Press, number 9780199257089.
    5. Daniel Kahneman & Richard H. Thaler, 2006. "Anomalies: Utility Maximization and Experienced Utility," Journal of Economic Perspectives, American Economic Association, vol. 20(1), pages 221-234, Winter.
    6. Jérôme Busemeyer & Peter Kvam & Ariane Lambert-Mogiliansky, 2014. "An Empirical Test of Type-Indeterminacy in the Prisoner's Dilemma," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-01053522, HAL.
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    Keywords

    Hilbert space of types; Type Indeterminacy; Superposition of preferences; Actions as projections; Cashing-on-the-go; Type Indeterminate Nash Equilibrium;

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