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Bayesian Persuasion with Costly Information Acquisition

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  • Ludmila Matyskova

Abstract

A sender who chooses a signal to reveal to a receiver can often influence the receiver’s subsequent actions. Is persuasion more difficult when the receiver has her own sources of information? Does the receiver benefit from having additional information sources? We consider a Bayesian persuasion model extended to a receiver’s endogenous acquisition of information under an entropy-based cost commonly used in rational inattention. A sender’s optimal signal can be computed from standard Bayesian persuasion subject to an additional constraint: the receiver never gathers her own costly information. We further determine a finite set of the sender’s signals satisfying the additional constraint in which some optimal signal must be contained. The set is characterized by linear conditions using the receiver’s utility and information cost parameters. The new method is also applicable to a standard Bayesian persuasion model and can simplify, sometimes dramatically, the search for a sender’s optimal signal (as opposed to a standard concavification technique used to solve these models). We show that the ‘threat’ of additional learning weakly decreases the sender’s expected equilibrium payoff. However, the outcome can be worse not only for the sender, but also for the receiver.

Suggested Citation

  • Ludmila Matyskova, 2018. "Bayesian Persuasion with Costly Information Acquisition," CERGE-EI Working Papers wp614, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
  • Handle: RePEc:cer:papers:wp614
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    References listed on IDEAS

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    1. Kolotilin, Anton, 2015. "Experimental design to persuade," Games and Economic Behavior, Elsevier, vol. 90(C), pages 215-226.
    2. Anne-Katrin Roesler & Balázs Szentes, 2017. "Buyer-Optimal Learning and Monopoly Pricing," American Economic Review, American Economic Association, vol. 107(7), pages 2072-2080, July.
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    4. Anton Kolotilin & Tymofiy Mylovanov & Andriy Zapechelnyuk & Ming Li, 2017. "Persuasion of a Privately Informed Receiver," Econometrica, Econometric Society, vol. 85(6), pages 1949-1964, November.
    5. Dirk Bergemann & Stephen Morris, 2016. "Information Design, Bayesian Persuasion, and Bayes Correlated Equilibrium," American Economic Review, American Economic Association, vol. 106(5), pages 586-591, May.
    6. Kolotilin, Anton, 2018. "Optimal information disclosure: a linear programming approach," Theoretical Economics, Econometric Society, vol. 13(2), May.
    7. Aoyagi, Masaki, 2014. "Strategic obscurity in the forecasting of disasters," Games and Economic Behavior, Elsevier, vol. 87(C), pages 485-496.
    8. de Oliveira, Henrique & Denti, Tommaso & Mihm, Maximilian & Ozbek, Kemal, 2017. "Rationally inattentive preferences and hidden information costs," Theoretical Economics, Econometric Society, vol. 12(2), May.
    9. Martin, Daniel, 2017. "Strategic pricing with rational inattention to quality," Games and Economic Behavior, Elsevier, vol. 104(C), pages 131-145.
    10. Gick, Wolfgang & Pausch, Thilo, 2012. "Persuasion by stress testing: Optimal disclosure of supervisory information in the banking sector," Discussion Papers 32/2012, Deutsche Bundesbank.
    11. Andrew Caplin & Mark Dean & John Leahy, 2017. "Rationally Inattentive Behavior: Characterizing and Generalizing Shannon Entropy," NBER Working Papers 23652, National Bureau of Economic Research, Inc.
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    Citations

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    Cited by:

    1. Robertson, Matthew J., 2018. "Wrongful Conviction, Persuasion and Loss Aversion," CRETA Online Discussion Paper Series 48, Centre for Research in Economic Theory and its Applications CRETA.
    2. Benjamin Balzer & Benjamin Young, 2020. "A Theory of Intuition and Contemplation," Working Paper Series 2020/01, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    3. Egorov, Georgy & Sonin, Konstantin, 2019. "Persuasion on Networks," CEPR Discussion Papers 13723, C.E.P.R. Discussion Papers.
    4. Mackowiak, Bartosz Adam & Matejka, Filip & Wiederholt, Mirko, 2020. "Rational Inattention: A Review," CEPR Discussion Papers 15408, C.E.P.R. Discussion Papers.
    5. Wei, Dong, 2021. "Persuasion under costly learning," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    6. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    7. Antler, Yair & Bird, Daniel & Oliveros, Santiago, 2019. "Sequential Learning," CEPR Discussion Papers 13934, C.E.P.R. Discussion Papers.
    8. Vasudha Jain & Mark Whitmeyer, 2019. "Competing to Persuade a Rationally Inattentive Agent," Papers 1907.09255, arXiv.org, revised Feb 2020.
    9. Kerman, Toygar & Herings, P. Jean-Jacques & Karos, Dominik, 2020. "Persuading Strategic Voters," Research Memorandum 004, Maastricht University, Graduate School of Business and Economics (GSBE).

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    More about this item

    Keywords

    Bayesian persuasion; rational inattention; costly information acquisition; information design;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • 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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