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Garbling of signals and outcome equivalence

Author

Listed:
  • Ehud Lehrer

    (TAU - School of Mathematical Sciences [Tel Aviv] - TAU - Raymond and Beverly Sackler Faculty of Exact Sciences [Tel Aviv] - TAU - Tel Aviv University)

  • Dinah Rosenberg

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique)

  • Eran Shmaya

    (Kellogg [Northwestern] - Kellogg School of Management [Northwestern University, Evanston] - Northwestern University [Evanston])

Abstract

In a game with incomplete information players receive stochastic signals about the state of nature. The distribution of the signals given the state of nature is determined by the information structure. Different information structures may induce different equilibria. Two information structures are equivalent from the perspective of a modeler, if they induce the same equilibrium outcomes. We characterize the situations in which two information structures are equivalent in terms of natural transformations, called garblings, from one structure to another. We study the notion of 'being equivalent to' in relation with three equilibrium concepts: Nash equilibrium, agent normal-form correlated equilibrium and the belief invariant Bayesian solution.

Suggested Citation

  • Ehud Lehrer & Dinah Rosenberg & Eran Shmaya, 2013. "Garbling of signals and outcome equivalence," Post-Print hal-01069192, HAL.
    • Handle: RePEc:hal:journl:hal-01069192
    DOI: 10.1016/j.geb.2013.05.005
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    Citations

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    Cited by:

    1. Mark Whitmeyer, 2020. "In Simple Communication Games, When Does Ex Ante Fact-Finding Benefit the Receiver?," Papers 2001.09387, arXiv.org.
    2. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    3. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    4. Taneva, Ina A, 2015. "Information Design," SIRE Discussion Papers 2015-50, Scottish Institute for Research in Economics (SIRE).
    5. de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    6. Wu, Wenhao, 2023. "A geometric Blackwell’s order," Economics Letters, Elsevier, vol. 226(C).
    7. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    8. David Lagziel & Ehud Lehrer & Tao Wang, 2025. "Comparison of Oracles: Part II," Papers 2511.04449, arXiv.org, revised Nov 2025.
    9. 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.
    10. Li, Jian & Zhou, Junjie, 2020. "Information order in monotone decision problems under uncertainty," Journal of Economic Theory, Elsevier, vol. 187(C).
    11. 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.
    12. Daehyun Kim, 2019. "Comparison of information structures in stochastic games with imperfect public monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 267-285, March.
    13. Martin Gregor, 2014. "Access fees for competing lobbies," Working Papers IES 2014/22, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2014.
    14. Ina Taneva, 2019. "Information Design," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 151-185, November.
    15. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.

    More about this item

    Keywords

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    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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