IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2505.15955.html

Comparison of Oracles

Author

Listed:
  • David Lagziel
  • Ehud Lehrer
  • Tao Wang

Abstract

We analyze incomplete-information games where an oracle publicly shares information with players. One oracle dominates another if, in every game, it can match the set of equilibrium outcomes induced by the latter. Distinct characterizations are provided for deterministic and stochastic signaling functions, based on simultaneous posterior matching, partition refinements, and common knowledge components. This study extends the work of Blackwell (1951) to games, and expands the study of Aumann (1976) on common knowledge, along with the companion Part II, which develops a theory of information loops.

Suggested Citation

  • David Lagziel & Ehud Lehrer & Tao Wang, 2025. "Comparison of Oracles," Papers 2505.15955, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2505.15955
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2505.15955
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Emir Kamenica, 2019. "Bayesian Persuasion and Information Design," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 249-272, August.
    2. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2013. "Dynamic sender–receiver games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 502-534.
    3. 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.
    4. Jacopo Bizzotto & Jesper Rüdiger & Adrien Vigier, 2021. "Dynamic Persuasion with Outside Information," American Economic Journal: Microeconomics, American Economic Association, vol. 13(1), pages 179-194, February.
    5. Yeon-Koo Che & Johannes Hörner, 2018. "Recommender Systems as Mechanisms for Social Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 871-925.
    6. 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).
    7. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    8. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2017. "Optimal dynamic information provision," Games and Economic Behavior, Elsevier, vol. 104(C), pages 329-349.
    9. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    10. Bernhard Ganglmair & Emanuele Tarantino, 2014. "Conversation with secrets," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 273-302, June.
    11. Peski, Marcin, 2008. "Comparison of information structures in zero-sum games," Games and Economic Behavior, Elsevier, vol. 62(2), pages 732-735, March.
    12. Jeffrey C. Ely & Martin Szydlowski, 2020. "Moving the Goalposts," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 468-506.
    13. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    2. Li, Xuelin & Szydlowski, Martin & Yu, Fangyuan, 2025. "Dynamic information design in an entry game," Journal of Economic Theory, Elsevier, vol. 226(C).
    3. David Lagziel & Ehud Lehrer & Tao Wang, 2025. "Comparison of Oracles: Part II," Papers 2511.04449, arXiv.org, revised Nov 2025.
    4. de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    5. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    6. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    7. Fabrizio Germano & Peio Zuazo-Garin, 2017. "Bounded rationality and correlated equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 595-629, August.
    8. Wu, Wenhao, 2023. "A geometric Blackwell’s order," Economics Letters, Elsevier, vol. 226(C).
    9. Itai Arieli & Yakov Babichenko & Dima Shaiderman & Xianwen Shi, 2025. "Persuading while Learning," Working Papers tecipa-791, University of Toronto, Department of Economics.
    10. Lehrer, Ehud & Rosenberg, Dinah & Shmaya, Eran, 2013. "Garbling of signals and outcome equivalence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 179-191.
    11. Aïd, René & Bonesini, Ofelia & Callegaro, Giorgia & Campi, Luciano, 2025. "Continuous-time persuasion by filtering," Journal of Economic Dynamics and Control, Elsevier, vol. 176(C).
    12. 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.
    13. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299R2, Cowles Foundation for Research in Economics, Yale University, revised Jul 2022.
    14. Aïd, René & Bonesini, Ofelia & Callegaro, Giorgia & Campi, Luciano, 2025. "Continuous-time persuasion by filtering," LSE Research Online Documents on Economics 127889, London School of Economics and Political Science, LSE Library.
    15. Dirk Bergemann & Stephen Morris, 2019. "Information Design: A Unified Perspective," Journal of Economic Literature, American Economic Association, vol. 57(1), pages 44-95, March.
    16. Makris, Miltiadis & Renou, Ludovic, 2023. "Information design in multi-stage games," Theoretical Economics, Econometric Society, vol. 18(4), November.
    17. Mira Frick & Ryota Iijima & Yuhta Ishii, 2021. "Learning Efficiency of Multi-Agent Information Structures," Cowles Foundation Discussion Papers 2299R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    18. Taneva, Ina A, 2015. "Information Design," SIRE Discussion Papers 2015-50, Scottish Institute for Research in Economics (SIRE).
    19. repec:upd:utmpwp:019 is not listed on IDEAS
    20. Liu, Qingmin, 2015. "Correlation and common priors in games with incomplete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 49-75.
    21. Nuta, Shunya, 2024. "Starting rough, Dynamic persuasion with partial information," Economics Letters, Elsevier, vol. 239(C).

    More about this item

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • P00 - Political Economy and Comparative Economic Systems - - General - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2505.15955. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.