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Wait or act now? Learning dynamics in stopping games

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  • Ekmekci, Mehmet
  • Maestri, Lucas

Abstract

A principal chooses when to terminate her relationship with an agent in a dynamic environment. The agent's type is his private information, and his actions are observed with noise. Both players are long-lived. We characterize the equilibrium payoffs and behavior of patient players by establishing an equivalence of equilibrium outcomes to the unique Nash equilibrium of a simple one-shot signaling game. A patient agent reveals virtually all information that influences the principal at the beginning of the game. Hence, reputation is rapidly built. Despite eliciting some information, the principal does not benefit from it.

Suggested Citation

  • Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    • Handle: RePEc:eee:jetheo:v:205:y:2022:i:c:s0022053122001314
    DOI: 10.1016/j.jet.2022.105541
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    References listed on IDEAS

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    1. Laffont, Jean-Jacques & Tirole, Jean, 1987. "Comparative statics of the optimal dynamic incentive contract," European Economic Review, Elsevier, vol. 31(4), pages 901-926, June.
    2. Gerardi, Dino & Maestri, Lucas, 2020. "Dynamic contracting with limited commitment and the ratchet effect," Theoretical Economics, Econometric Society, vol. 15(2), May.
    3. Doval, Laura & Skreta, Vasiliki, 2024. "Optimal mechanism for the sale of a durable good," Theoretical Economics, Econometric Society, vol. 19(2), May.
    4. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    5. Atakan, Alp E. & Ekmekci, Mehmet, 2015. "Reputation in the long-run with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 553-605.
    6. Cripps, Martin W. & Dekel, Eddie & Pesendorfer, Wolfgang, 2005. "Reputation with equal discounting in repeated games with strictly conflicting interests," Journal of Economic Theory, Elsevier, vol. 121(2), pages 259-272, April.
    7. Qingmin Liu & Konrad Mierendorff & Xianwen Shi & Weijie Zhong, 2019. "Auctions with Limited Commitment," American Economic Review, American Economic Association, vol. 109(3), pages 876-910, March.
    8. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    9. Raymond Deneckere & Meng-Yu Liang, 2006. "Bargaining with Interdependent Values," Econometrica, Econometric Society, vol. 74(5), pages 1309-1364, September.
    10. Drew Fudenberg & David K. Levine, 2008. "Maintaining a Reputation when Strategies are Imperfectly Observed," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 8, pages 143-161, World Scientific Publishing Co. Pte. Ltd..
    11. Avidit Acharya & Juan Ortner, 2017. "Progressive Learning," Econometrica, Econometric Society, vol. 85(6), pages 1965-1990, November.
    12. Eduardo Faingold & Yuliy Sannikov, 2011. "Reputation in Continuous‐Time Games," Econometrica, Econometric Society, vol. 79(3), pages 773-876, May.
    13. Olivier Gossner, 2011. "Simple bounds on the value of a reputation," PSE-Ecole d'économie de Paris (Postprint) halshs-00654683, HAL.
    14. Alp E. Atakan & Mehmet Ekmekci, 2012. "Reputation in Long-Run Relationships," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 79(2), pages 451-480.
    15. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, September.
    16. Jean-Jacques Laffont & Jean Tirole, 1993. "A Theory of Incentives in Procurement and Regulation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121743, December.
    17. Gul, Faruk & Sonnenschein, Hugo & Wilson, Robert, 1986. "Foundations of dynamic monopoly and the coase conjecture," Journal of Economic Theory, Elsevier, vol. 39(1), pages 155-190, June.
    18. Ekmekci, Mehmet & Maestri, Lucas, 2019. "Reputation and screening in a noisy environment with irreversible actions," MPRA Paper 100885, University Library of Munich, Germany.
    19. Laffont, Jean-Jacques & Tirole, Jean, 1988. "The Dynamics of Incentive Contracts," Econometrica, Econometric Society, vol. 56(5), pages 1153-1175, September.
    20. Vasiliki Skreta, 2006. "Sequentially Optimal Mechanisms -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1085-1111.
    21. Marcin Pęski & Juuso Toikka, 2017. "Value of Persistent Information," Econometrica, Econometric Society, vol. 85(6), pages 1921-1948, November.
    22. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
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    More about this item

    Keywords

    Dynamic games; Reputation dynamics; Imperfect monitoring;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • 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
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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