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Information transmission in nested sender–receiver games

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  • Ying Chen
  • Sidartha Gordon

Abstract

We introduce a “nestedness” relation for a general class of sender–receiver games and compare equilibrium properties, in particular the amount of information transmitted, across games that are nested. Roughly, game $$B$$ B is nested in game $$A$$ A if the players’ optimal actions are closer in game $$B$$ B . We show that under some conditions, more information is transmitted in the nested game in the sense that the receiver’s expected equilibrium payoff is higher. The results generalize the comparative statics and welfare comparisons with respect to preferences in the seminal paper of Crawford and Sobel (Econometrica 50(6):1431–1452, 1982 ). We also derive new results with respect to changes in priors in addition to changes in preferences. We illustrate the usefulness of the results in three applications: (i) delegation to an intermediary with a different prior, (ii) the choice between centralization and delegation, and (iii) two-way communication with an informed principal. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Ying Chen & Sidartha Gordon, 2015. "Information transmission in nested sender–receiver games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 543-569, April.
    • Handle: RePEc:spr:joecth:v:58:y:2015:i:3:p:543-569
    DOI: 10.1007/s00199-014-0831-1
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    2. Frug, Alexander, 2016. "A note on optimal cheap talk equilibria in a discrete state space," Games and Economic Behavior, Elsevier, vol. 99(C), pages 180-185.
    3. Dilmé, Francesc, 2022. "Strategic communication with a small conflict of interest," Games and Economic Behavior, Elsevier, vol. 134(C), pages 1-19.
    4. Oded Berman & Mohammad M. Fazel-Zarandi & Dmitry Krass, 2019. "Truthful Cheap Talk: Why Operational Flexibility May Lead to Truthful Communication," Management Science, INFORMS, vol. 65(4), pages 1624-1641, April.
    5. Catonini, Emiliano & Stepanov, Sergey, 2023. "Reputation and information aggregation," Journal of Economic Behavior & Organization, Elsevier, vol. 208(C), pages 156-173.
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    8. Kellner, Christian & Le Quement, Mark T., 2018. "Endogenous ambiguity in cheap talk," Journal of Economic Theory, Elsevier, vol. 173(C), pages 1-17.

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    More about this item

    Keywords

    Sender–receiver games; Information transmission; Nestedness; Intermediary; Delegation; Informed principal; D23; D82; D83;
    All these keywords.

    JEL classification:

    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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