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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.

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

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    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.
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    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

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