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The relationship between quantum and classical correlation in games

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  • Brandenburger, Adam

Abstract

Quantum games have been argued to differ from classical games by virtue of the quantum-mechanical phenomenon of entanglement. We formulate a baseline of classical correlation - which takes two forms according as signals added to the game are or are not required to be independent of chance moves in the underlying game. We show that independence is a necessary condition for the addition of quantum signals to have a different effect from the addition of classical signals.

Suggested Citation

  • Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
    • Handle: RePEc:eee:gamebe:v:69:y:2010:i:1:p:175-183
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    References listed on IDEAS

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    1. Vladislav Kargin, 2008. "On coordination games with quantum correlations," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 211-218, June.
    2. Pierfrancesco La Mura, 2003. "Correlated Equilibria of Classical Strategic Games with Quantum Signals," Papers quant-ph/0309033, arXiv.org.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
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    5. Adam Brandenburger & Amanda Friedenberg, 2014. "Intrinsic Correlation in Games," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 4, pages 59-111, World Scientific Publishing Co. Pte. Ltd..
    6. Bernardo A. Huberman & Tad Hogg HP Laboratories, 2003. "Quantum Solution of Coordination Problems," Game Theory and Information 0306005, University Library of Munich, Germany.
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    Cited by:

    1. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    2. Luca Lambertini, 2013. "John von Neumann between Physics and Economics: A methodological note," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 5(2), pages 177-189, December.
    3. Ariane Lambert-Mogiliansky & Ismael Martinez-Martinez, 2014. "Basic Framework for Games with Quantum-like Players," Working Papers hal-01095472, HAL.
    4. Ismaël Rafaï & Sébastien Duchêne & Eric Guerci & Irina Basieva & Andrei Khrennikov, 2022. "The triple-store experiment: a first simultaneous test of classical and quantum probabilities in choice over menus," Theory and Decision, Springer, vol. 92(2), pages 387-406, March.
    5. Thomas Boyer-Kassem & Sébastien Duchêne & Eric Guerci, 2016. "Quantum-like models cannot account for the conjunction fallacy," Theory and Decision, Springer, vol. 81(4), pages 479-510, November.
    6. Hanauske, Matthias & Kunz, Jennifer & Bernius, Steffen & König, Wolfgang, 2010. "Doves and hawks in economics revisited: An evolutionary quantum game theory based analysis of financial crises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 5084-5102.
    7. Basieva, Irina & Khrennikova, Polina & Pothos, Emmanuel M. & Asano, Masanari & Khrennikov, Andrei, 2018. "Quantum-like model of subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 150-162.
    8. Ariane Lambert-Mogiliansky & Ismael Martinez-Martinez, 2014. "Basic Framework for Games with Quantum-like Players," PSE Working Papers hal-01095472, HAL.
    9. Haven, Emmanuel & Khrennikova, Polina, 2018. "A quantum-probabilistic paradigm: Non-consequential reasoning and state dependence in investment choice," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 186-197.

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