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Correlation and common priors in games with incomplete information

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  • Liu, Qingmin

Abstract

This paper provides an explicit characterization of correlations that are implicitly captured by partition models for incomplete information games. The main result of this paper shows that every partition model for incomplete information can be decomposed into the conjunctions of a unique non-redundant model and a unique “individually uninformative” correlating device. The separation of the correlating device from the underlying non-redundant model allows us to separate their strategic implications. As an application, we use this correlation device to define correlated equilibria. Separating the common-prior property of the correlating devices from the underlying state space sheds light on the difference between interim independent and correlated rationalizability.

Suggested Citation

  • Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    • Handle: RePEc:eee:jetheo:v:157:y:2015:i:c:p:49-75
    DOI: 10.1016/j.jet.2014.09.010
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    References listed on IDEAS

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    1. Liu, Qingmin, 2009. "On redundant types and Bayesian formulation of incomplete information," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2115-2145, September.
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    16. 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..
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    Cited by:

    1. Bergemann, Dirk & Morris, Stephen, 2017. "Belief-free rationalizability and informational robustness," Games and Economic Behavior, Elsevier, vol. 104(C), pages 744-759.
    2. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    3. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    4. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    5. Stephen Morris & Takashi Ui, 2025. "Incomplete Information Robustness," Papers 2502.19075, arXiv.org, revised Feb 2025.
    6. Larionov, Daniil & Pham, Hien & Yamashita, Takuro & Zhu, Shuguang, 2021. "First Best Implementation with Costly Information Acquisition," TSE Working Papers 21-1261, Toulouse School of Economics (TSE), revised Apr 2022.
    7. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2022. "Counterfactuals with Latent Information," American Economic Review, American Economic Association, vol. 112(1), pages 343-368, January.
    8. Gabriel Ziegler, 2021. "Informational Robustness of Common Belief in Rationality," Papers 2103.02402, arXiv.org, revised Feb 2022.
    9. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    10. repec:upd:utmpwp:019 is not listed on IDEAS
    11. Zhu, Shuguang, 2023. "Private disclosure with multiple agents," Journal of Economic Theory, Elsevier, vol. 212(C).
    12. Ziegler, Gabriel, 2022. "Informational robustness of common belief in rationality," Games and Economic Behavior, Elsevier, vol. 132(C), pages 592-597.
    13. Cédric Wanko, 2018. "A Unique and Stable $$\hbox {Se}{\mathcal {C}}\hbox {ure}$$ Se C ure Reversion Protocol Improving Efficiency: A Computational Bayesian Approach for Empirical Analysis," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 1-23, June.

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    More about this item

    Keywords

    Correlation; Common prior; Correlated equilibrium; Interim rationalizability; Redundant types;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General

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