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Quantum Bayes Correlated Equilibrium and the Comparison of Quantum Information Structures in Games

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  • Furkan Sezer

Abstract

Bergemann and Morris (2016) show that one information structure is more informative than another exactly when it induces a smaller set of Bayes correlated equilibrium outcomes in every game. We build the quantum analogue. An information structure becomes a family of density operators indexed by the payoff state, which the mediator observes. We show that obedience is equivalent to a Loewner domination between operators on one player's subsystem. The equilibrium set is then a nonempty compact spectrahedron computable by semidefinite programming, classical structures embed exactly, and under quantum individual sufficiency more information shrinks the equilibrium set in every game.

Suggested Citation

  • Furkan Sezer, 2026. "Quantum Bayes Correlated Equilibrium and the Comparison of Quantum Information Structures in Games," Papers 2608.04973, arXiv.org.
    • Handle: RePEc:arx:papers:2608.04973
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    References listed on IDEAS

    as
    1. Françoise Forges, 2006. "Correlated Equilibrium in Games with Incomplete Information Revisited," Theory and Decision, Springer, vol. 61(4), pages 329-344, December.
    2. Dirk Bergemann & Stephen Morris, 2016. "Information Design, Bayesian Persuasion, and Bayes Correlated Equilibrium," American Economic Review, American Economic Association, vol. 106(5), pages 586-591, May.
    3. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    4. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    5. Robert J. Aumann, 2025. "Correlated Equilibrium as an Expression of Bayesian Rationality," World Scientific Book Chapters, in: SELECTED CONTRIBUTIONS TO GAME THEORY, chapter 7, pages 175-200, World Scientific Publishing Co. Pte. Ltd..
    6. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2010. "Signaling and mediation in games with common interests," Games and Economic Behavior, Elsevier, vol. 68(2), pages 670-682, March.
    7. FORGES , Françoise, 1993. "Five Legitimate Definitions of Correlated Equilibrium in Games with Incomplete Information," LIDAM Discussion Papers CORE 1993009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    9. repec:dau:papers:123456789/157 is not listed on IDEAS
    10. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    11. Holevo, A. S., 1973. "Statistical decision theory for quantum systems," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 337-394, December.
    12. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
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