IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2007.15514.html
   My bibliography  Save this paper

Signaling with Private Monitoring

Author

Listed:
  • Gonzalo Cisternas
  • Aaron Kolb

Abstract

We study dynamic signaling when the informed party does not observe the signals generated by her actions. A long-run player signals her type continuously over time to a myopic second player who privately monitors her behavior; in turn, the myopic player transmits his private inferences back through an imperfect public signal of his actions. Preferences are linear-quadratic and the information structure is Gaussian. We construct linear Markov equilibria using belief states up to the long-run player's $\textit{second-order belief}$. Because of the private monitoring, this state is an explicit function of the long-run player's past play. A novel separation effect then emerges through this second-order belief channel, altering the traditional signaling that arises when beliefs are public. Applications to models of leadership, reputation, and trading are examined.

Suggested Citation

  • Gonzalo Cisternas & Aaron Kolb, 2020. "Signaling with Private Monitoring," Papers 2007.15514, arXiv.org.
    • Handle: RePEc:arx:papers:2007.15514
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2007.15514
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:cwl:cwldpp:1953rrr is not listed on IDEAS
    2. repec:cwl:cwldpp:1953rr is not listed on IDEAS
    3. Bergemann, Dirk & Strack, Philipp, 2015. "Dynamic revenue maximization: A continuous time approach," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 819-853.
    4. Carlsson, Hans & Dasgupta, Sudipto, 1997. "Noise-Proof Equilibria in Two-Action Signaling Games," Journal of Economic Theory, Elsevier, vol. 77(2), pages 432-460, December.
    5. Kolb, Aaron M., 2019. "Strategic real options," Journal of Economic Theory, Elsevier, vol. 183(C), pages 344-383.
    6. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    7. Alessandro Bonatti & Gonzalo Cisternas, 2020. "Consumer Scores and Price Discrimination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 87(2), pages 750-791.
    8. Mailath, George J. & Morris, Stephen, 2002. "Repeated Games with Almost-Public Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 189-228, January.
    9. Heikki Rantakari, 2008. "Governing Adaptation -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(4), pages 1257-1285.
    10. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    11. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    12. Hermalin, Benjamin E, 1998. "Toward an Economic Theory of Leadership: Leading by Example," American Economic Review, American Economic Association, vol. 88(5), pages 1188-1206, December.
    13. Nick Feltovich & Richmond Harbaugh & Ted To, 2002. "Too Cool for School? Signalling and Countersignalling," RAND Journal of Economics, The RAND Corporation, vol. 33(4), pages 630-649, Winter.
    14. Yuliy Sannikov, 2007. "Games with Imperfectly Observable Actions in Continuous Time," Econometrica, Econometric Society, vol. 75(5), pages 1285-1329, September.
    15. J. Marschak, 1955. "Elements for a Theory of Teams," Management Science, INFORMS, vol. 1(2), pages 127-137, January.
    16. Kandori, Michihiro, 2002. "Introduction to Repeated Games with Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 1-15, January.
    17. Kerry Back & C. Henry Cao & Gregory A. Willard, 2000. "Imperfect Competition among Informed Traders," Journal of Finance, American Finance Association, vol. 55(5), pages 2117-2155, October.
    18. Eduardo Faingold & Yuliy Sannikov, 2011. "Reputation in Continuous‐Time Games," Econometrica, Econometric Society, vol. 79(3), pages 773-876, May.
    19. Matthews, Steven A & Mirman, Leonard J, 1983. "Equilibrium Limit Pricing: The Effects of Private Information and Stochastic Demand," Econometrica, Econometric Society, vol. 51(4), pages 981-996, July.
    20. Alessandro Bonatti & Gonzalo Cisternas & Juuso Toikka, 2017. "Dynamic Oligopoly with Incomplete Information," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 503-546.
    21. Foster, F. Douglas & Viswanathan, S., 1994. "Strategic Trading with Asymmetrically Informed Traders and Long-Lived Information," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(4), pages 499-518, December.
    22. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    23. Sander Heinsalu, 2018. "Dynamic Noisy Signaling," American Economic Journal: Microeconomics, American Economic Association, vol. 10(2), pages 225-249, May.
    24. Wouter Dessein & Tano Santos, 2006. "Adaptive Organizations," Journal of Political Economy, University of Chicago Press, vol. 114(5), pages 956-985, October.
    25. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    26. Townsend, Robert M, 1983. "Forecasting the Forecasts of Others," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 546-588, August.
    27. Kremer, Ilan & Skrzypacz, Andrzej, 2007. "Dynamic signaling and market breakdown," Journal of Economic Theory, Elsevier, vol. 133(1), pages 58-82, March.
    28. Brendan Daley & Brett Green, 2012. "Waiting for News in the Market for Lemons," Econometrica, Econometric Society, vol. 80(4), pages 1433-1504, July.
    29. Gonzalo Cisternas, 2018. "Two-Sided Learning and the Ratchet Principle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(1), pages 307-351.
    30. Luis Garicano, 2000. "Hierarchies and the Organization of Knowledge in Production," Journal of Political Economy, University of Chicago Press, vol. 108(5), pages 874-904, October.
    31. Christopher Phelan & Andrzej Skrzypacz, 2012. "Beliefs and Private Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(4), pages 1637-1660.
    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. Dilmé, Francesc, 2019. "Dynamic quality signaling with hidden actions," Games and Economic Behavior, Elsevier, vol. 113(C), pages 116-136.
    2. , H. & ,, 2016. "Approximate efficiency in repeated games with side-payments and correlated signals," Theoretical Economics, Econometric Society, vol. 11(1), January.
    3. Daley, Brendan & Green, Brett, 2014. "Market signaling with grades," Journal of Economic Theory, Elsevier, vol. 151(C), pages 114-145.
    4. Yamamoto, Yuichi, 2012. "Characterizing belief-free review-strategy equilibrium payoffs under conditional independence," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1998-2027.
    5. Yamamoto, Yuichi, 2009. "A limit characterization of belief-free equilibrium payoffs in repeated games," Journal of Economic Theory, Elsevier, vol. 144(2), pages 802-824, March.
    6. Asriyan, Vladimir & Fuchs, William & Green, Brett, 2021. "Aggregation and design of information in asset markets with adverse selection," Journal of Economic Theory, Elsevier, vol. 191(C).
    7. , J. & ,, 2006. "Coordination failure in repeated games with almost-public monitoring," Theoretical Economics, Econometric Society, vol. 1(3), pages 311-340, September.
    8. Doruk Cetemen & Gonzalo Cisternas & Aaron Kolb & S Viswanathan, 2022. "Leader-Follower Dynamics in Shareholder Activism," Staff Reports 1030, Federal Reserve Bank of New York.
    9. Solan, Eilon & Zhao, Chang, 2023. "When (not) to publicize inspection results," Journal of Economic Theory, Elsevier, vol. 210(C).
    10. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    11. Michihiro Kandori, 2011. "Weakly Belief‐Free Equilibria in Repeated Games With Private Monitoring," Econometrica, Econometric Society, vol. 79(3), pages 877-892, May.
    12. Yuichi Yamamoto, 2013. "Individual Learning and Cooperation in Noisy Repeated Games," PIER Working Paper Archive 13-038, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    13. Sugaya, Takuo & Yamamoto, Yuichi, 2020. "Common learning and cooperation in repeated games," Theoretical Economics, Econometric Society, vol. 15(3), July.
    14. Vladimir Asriyan, 2017. "Information Aggregation in Dynamic Markets with Adverse Selection," 2017 Meeting Papers 988, Society for Economic Dynamics.
    15. Heller, Yuval, 2015. "Instability of Equilibria with Imperfect Private Monitoring," MPRA Paper 64468, University Library of Munich, Germany.
    16. repec:pra:mprapa:64485 is not listed on IDEAS
    17. Takuo Sugaya & Yuichi Yamamoto, 2019. "Common Learning and Cooperation in Repeated Games," PIER Working Paper Archive 19-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    18. Katayama, Hajime & Meagher, Kieron J. & Wait, Andrew, 2018. "Authority and communication in firms," Journal of Economic Behavior & Organization, Elsevier, vol. 155(C), pages 315-348.
    19. Cetemen, D. & Cisternas, G. & Kolb, A. & Viswanathan, S., 2022. "Activist Manipulation Dynamics," Working Papers 22/04, Department of Economics, City University London.
    20. Chen, Bo, 2010. "A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring," Journal of Economic Theory, Elsevier, vol. 145(1), pages 402-420, January.
    21. Ashkenazi-Golan, Galit & Lehrer, Ehud, 2019. "What you get is what you see: Cooperation in repeated games with observable payoffs," Journal of Economic Theory, Elsevier, vol. 181(C), pages 197-237.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • 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

    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:2007.15514. 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.