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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 School of Management - Northwestern University)

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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    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, 2013. "Robust Predictions in Games With Incomplete Information," Econometrica, Econometric Society, vol. 81(4), pages 1251-1308, July.
    3. Aumann, Robert J, 1987. "Correlated Equilibrium as an Expression of Bayesian Rationality," Econometrica, Econometric Society, vol. 55(1), pages 1-18, January.
    4. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    5. repec:cwl:cwldpp:1821rrr is not listed on IDEAS
    6. Hirshleifer, Jack, 1971. "The Private and Social Value of Information and the Reward to Inventive Activity," American Economic Review, American Economic Association, vol. 61(4), pages 561-574, September.
    7. repec:dau:papers:123456789/157 is not listed on IDEAS
    8. Cotter, Kevin D., 1991. "Correlated equilibrium in games with type-dependent strategies," Journal of Economic Theory, Elsevier, vol. 54(1), pages 48-68, June.
    9. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    10. Peski, Marcin, 2008. "Comparison of information structures in zero-sum games," Games and Economic Behavior, Elsevier, vol. 62(2), pages 732-735, March.
    11. 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.
    12. Igal Milchtaich, 2009. "Implementability of Correlated and Communication Equilibrium Outcomes in Incomplete Information Games," Working Papers 2009-27, Bar-Ilan University, Department of Economics.
    13. Gossner, Olivier, 2000. "Comparison of Information Structures," Games and Economic Behavior, Elsevier, vol. 30(1), pages 44-63, January.
    14. , C. & ,, 2006. "Hierarchies of belief and interim rationalizability," Theoretical Economics, Econometric Society, vol. 1(1), pages 19-65, March.
    15. 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).
    16. FORGES, Françoise, 1986. "Correlated equilibria in repeated games with lack of information on one side: a model with verifiable types," LIDAM Reprints CORE 700, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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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. Bergemann, Dirk & Morris, Stephen, 2016. "Bayes correlated equilibrium and the comparison of information structures in games," Theoretical Economics, Econometric Society, vol. 11(2), May.
    3. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    4. Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    5. Taneva, Ina A, 2015. "Information Design," SIRE Discussion Papers 2015-50, Scottish Institute for Research in Economics (SIRE).
    6. 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.
    7. de Oliveira, Henrique, 2018. "Blackwell's informativeness theorem using diagrams," Games and Economic Behavior, Elsevier, vol. 109(C), pages 126-131.
    8. Li, Jian & Zhou, Junjie, 2020. "Information order in monotone decision problems under uncertainty," Journal of Economic Theory, Elsevier, vol. 187(C).
    9. Wu, Wenhao, 2023. "A geometric Blackwell’s order," Economics Letters, Elsevier, vol. 226(C).
    10. 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.
    11. 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.
    12. 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.
    13. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    14. Ina Taneva, 2019. "Information Design," American Economic Journal: Microeconomics, American Economic Association, vol. 11(4), pages 151-185, November.

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    More about this item

    Keywords

    Incomplete information; Information structure; Correlated equilibrium; Garbling; Robustness;
    All these keywords.

    JEL classification:

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

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