IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2207.02744.html
   My bibliography  Save this paper

Reputation Effects under Short Memories

Author

Listed:
  • Harry Pei

Abstract

I analyze a novel reputation game between a patient seller and a sequence of myopic consumers, in which the consumers have limited memories and do not know the exact sequence of the seller's actions. I focus on the case where each consumer only observes the number of times that the seller took each of his actions in the last K periods. When payoffs are monotone-supermodular, I show that the patient seller can approximately secure his commitment payoff in all equilibria as long as K is at least one. I also show that the consumers can approximately attain their first-best welfare in all equilibria if and only if their memory length K is lower than some cutoff. Although a longer memory enables more consumers to punish the seller once the seller shirks, it weakens their incentives to punish the seller once they observe him shirking

Suggested Citation

  • Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    • Handle: RePEc:arx:papers:2207.02744
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2207.02744
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yingkai Li & Harry Pei, 2020. "Equilibrium Behaviors in Repeated Games," Papers 2007.14002, arXiv.org, revised Feb 2021.
    2. Fudenberg, Drew & Tirole, Jean, 1991. "Perfect Bayesian equilibrium and sequential equilibrium," Journal of Economic Theory, Elsevier, vol. 53(2), pages 236-260, April.
    3. Li, Yingkai & Pei, Harry, 2021. "Equilibrium behaviors in repeated games," Journal of Economic Theory, Elsevier, vol. 193(C).
    4. Ekmekci, Mehmet & Gossner, Olivier & Wilson, Andrea, 2012. "Impermanent types and permanent reputations," Journal of Economic Theory, Elsevier, vol. 147(1), pages 162-178.
    5. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, September.
    6. Kaya, Ayça & Roy, Santanu, 2022. "Market screening with limited records," Games and Economic Behavior, Elsevier, vol. 132(C), pages 106-132.
    7. Yuval Heller & Erik Mohlin, 2018. "Observations on Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2253-2282.
    8. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
    9. Echenique, Federico, 2004. "Extensive-form games and strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 348-364, February.
    10. Philippe Jehiel & Larry Samuelson, 2012. "Reputation with Analogical Reasoning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(4), pages 1927-1969.
    11. Ekmekci, Mehmet, 2011. "Sustainable reputations with rating systems," Journal of Economic Theory, Elsevier, vol. 146(2), pages 479-503, March.
    12. 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..
    13. V Bhaskar & Caroline Thomas, 2019. "Community Enforcement of Trust with Bounded Memory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(3), pages 1010-1032.
    14. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2004. "Imperfect Monitoring and Impermanent Reputations," Econometrica, Econometric Society, vol. 72(2), pages 407-432, March.
    15. Parikshit Ghosh & Debraj Ray, 1996. "Cooperation in Community Interaction Without Information Flows," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 491-519.
    16. 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..
    17. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. John K.‐H. Quah & Bruno Strulovici, 2012. "Aggregating the Single Crossing Property," Econometrica, Econometric Society, vol. 80(5), pages 2333-2348, September.
    19. Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    20. Takuo Sugaya & Alexander Wolitzky, 2020. "A Few Bad Apples Spoil the Barrel: An Anti-folk Theorem for Anonymous Repeated Games with Incomplete Information," American Economic Review, American Economic Association, vol. 110(12), pages 3817-3835, December.
    21. Paul Niehaus, 2011. "Filtered Social Learning," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 686-720.
    22. Qingmin Liu, 2011. "Information Acquisition and Reputation Dynamics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(4), pages 1400-1425.
    23. Olivier Gossner, 2011. "Simple bounds on the value of a reputation," PSE-Ecole d'économie de Paris (Postprint) halshs-00654683, HAL.
    24. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 63-80.
    25. Joyee Deb, 2020. "Cooperation and Community Responsibility," Journal of Political Economy, University of Chicago Press, vol. 128(5), pages 1976-2009.
    26. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    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. Harry Pei, 2020. "Reputation Building under Observational Learning," Papers 2006.08068, arXiv.org, revised Nov 2020.
    2. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    4. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
    5. Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    6. Heski Bar-Isaac Jr. & Joyee Deb Jr., 2014. "(Good and Bad) Reputation for a Servant of Two Masters," American Economic Journal: Microeconomics, American Economic Association, vol. 6(4), pages 293-325, November.
    7. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    8. Li, Yingkai & Pei, Harry, 2021. "Equilibrium behaviors in repeated games," Journal of Economic Theory, Elsevier, vol. 193(C).
    9. Harry Pei, 2020. "Reputation for Playing Mixed Actions: A Characterization Theorem," Papers 2006.16206, arXiv.org, revised Apr 2021.
    10. Ekmekci, Mehmet & Gossner, Olivier & Wilson, Andrea, 2012. "Impermanent types and permanent reputations," Journal of Economic Theory, Elsevier, vol. 147(1), pages 162-178.
    11. Monte, Daniel, 2013. "Bounded memory and permanent reputations," Journal of Mathematical Economics, Elsevier, vol. 49(5), pages 345-354.
    12. Nuh Aygün Dalkıran, 2016. "Order of limits in reputations," Theory and Decision, Springer, vol. 81(3), pages 393-411, September.
    13. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    14. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    15. Wiseman, Thomas, 2008. "Reputation and impermanent types," Games and Economic Behavior, Elsevier, vol. 62(1), pages 190-210, January.
    16. Pei, Harry, 2023. "Repeated communication with private lying costs," Journal of Economic Theory, Elsevier, vol. 210(C).
    17. Sharma, Priyanka, 2017. "Is more information always better? A case in credit markets," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 269-283.
    18. David K. Levine, 2021. "The Reputation Trap," Econometrica, Econometric Society, vol. 89(6), pages 2659-2678, November.
    19. Pei, Harry, 2022. "Reputation for playing mixed actions: A characterization theorem," Journal of Economic Theory, Elsevier, vol. 201(C).
    20. Kaya, Ayça & Roy, Santanu, 2022. "Market screening with limited records," Games and Economic Behavior, Elsevier, vol. 132(C), pages 106-132.

    More about this item

    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:2207.02744. 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.