IDEAS home Printed from https://ideas.repec.org/p/nwu/cmsems/1506.html
   My bibliography  Save this paper

Reputation in the Long-Run with Imperfect Monitoring

Author

Listed:
  • Alp Atakan
  • Mehmet Ekmekci

Abstract

We study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stagegame actions of player two imperfectly, while player two monitors the pure stagegame actions of player one perfectly. Player one’s type is private information and he may be a “commitment type,” drawn from a countable set of commitment types, who is locked into playing a particular strategy. Under a full-support assumption on the monitoring structure, we prove a reputation result for games with locally nonconflicting interests or games with strictly conflicting interests: if there is positive probability that player one is a particular type whose commitment payoff is equal to player one’s highest payoff, consistent with the players’ individual rationality, then a patient player one secures this type’s commitment payoff in any Bayes-Nash equilibrium of the repeated game. In contrast, if the type’s commitment payoff is strictly less than player one’s highest payoff consistent with the players’ individual rationality, then the worst perfect Bayesian equilibrium payoff for a patient player one is equal to his minimax payoff.

Suggested Citation

  • Alp Atakan & Mehmet Ekmekci, 2009. "Reputation in the Long-Run with Imperfect Monitoring," Discussion Papers 1506, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1506
    as

    Download full text from publisher

    File URL: http://www.kellogg.northwestern.edu/faculty/ekmekci/personal/assets/reputation%20imperfect%20monitoring.pdf
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. 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.
    3. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
    4. 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..
    5. Cripps, Martin W & Thomas, Jonathan P, 1995. "Reputation and Commitment in Two-Person Repeated Games without Discounting," Econometrica, Econometric Society, vol. 63(6), pages 1401-1419, November.
    6. Drew Fudenberg & David Levine & Eric Maskin, 2008. "The Folk Theorem With Imperfect Public Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 12, pages 231-273, World Scientific Publishing Co. Pte. Ltd..
    7. 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..
    8. Aoyagi, Masaki, 1996. "Reputation and Dynamic Stackelberg Leadership in Infinitely Repeated Games," Journal of Economic Theory, Elsevier, vol. 71(2), pages 378-393, November.
    9. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in Perturbed Repeated Games," Journal of Economic Theory, Elsevier, vol. 69(2), pages 387-410, May.
    10. Cripps, Martin W. & Thomas, Jonathan P., 1997. "Reputation and Perfection in Repeated Common Interest Games," Games and Economic Behavior, Elsevier, vol. 18(2), pages 141-158, February.
    11. Marco Celentani & Drew Fudenberg & David K. Levine & Wolfgang Pesendorfer, 2008. "Maintaining A Reputation Against A Long-Lived Opponent," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 9, pages 163-176, World Scientific Publishing Co. Pte. Ltd..
    12. Atakan, Alp Enver & Ekmekci, Mehmet, 2014. "Reputation in Repeated Moral Hazard Games," MPRA Paper 54427, University Library of Munich, Germany.
    13. Olivier Gossner, 2011. "Simple bounds on the value of a reputation," PSE-Ecole d'économie de Paris (Postprint) halshs-00654683, HAL.
    14. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
    15. 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.
    16. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, September.
    17. Martin W. Cripps & Jonathan P. Thomas, 2003. "Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 433-462, August.
    18. Robert Evans & Jonathan P. Thomas, 1997. "Reputation and Experimentation in Repeated Games with Two Long-Run Players," Econometrica, Econometric Society, vol. 65(5), pages 1153-1174, September.
    19. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cesi Berardino & Iozzi Alberto & Valentini Edilio, 2012. "Regulating Unverifiable Quality by Fixed-Price Contracts," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 12(1), pages 1-39, September.
    2. Ekmekci, Mehmet & Maestri, Lucas, 2019. "Reputation and screening in a noisy environment with irreversible actions," MPRA Paper 100885, University Library of Munich, Germany.
    3. Nuh Aygün Dalkıran, 2016. "Order of limits in reputations," Theory and Decision, Springer, vol. 81(3), pages 393-411, September.
    4. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    5. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    6. 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.
    7. Atakan, Alp Enver & Ekmekci, Mehmet, 2014. "Reputation in Repeated Moral Hazard Games," MPRA Paper 54427, University Library of Munich, Germany.
    8. Monte, Daniel, 2016. "Reputation with one-sided monitoring: Ignorance as a commitment device," Economics Letters, Elsevier, vol. 144(C), pages 18-21.
    9. Drew Fudenberg & Ying Gao & Harry Pei, 2020. "A Reputation for Honesty," Papers 2011.07159, arXiv.org.

    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. Atakan, Alp Enver & Ekmekci, Mehmet, 2014. "Reputation in Repeated Moral Hazard Games," MPRA Paper 54427, University Library of Munich, Germany.
    2. Wolitzky, Alexander, 2011. "Indeterminacy of reputation effects in repeated games with contracts," Games and Economic Behavior, Elsevier, vol. 73(2), pages 595-607.
    3. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    4. Monte, Daniel, 2016. "Reputation with one-sided monitoring: Ignorance as a commitment device," Economics Letters, Elsevier, vol. 144(C), pages 18-21.
    5. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
    6. Harry Pei, 2020. "Reputation Building under Observational Learning," Papers 2006.08068, arXiv.org, revised Nov 2020.
    7. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    8. Joyee Deb & Yuhta Ishii, 2016. "Reputation Building under Uncertain Monitoring," Cowles Foundation Discussion Papers 2042, Cowles Foundation for Research in Economics, Yale University.
    9. Yuval Heller & Erik Mohlin, 2018. "Observations on Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2253-2282.
    10. Françoise Forges, 2012. "Folk theorems for Bayesian (public good) games," Post-Print hal-02447604, HAL.
    11. Dilip Abreu & David G. Pearce, 2006. "Bargaining, Reputation and Equilibrium Selection in Repeated Games with Contracts," Levine's Bibliography 321307000000000640, UCLA Department of Economics.
    12. 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.
    13. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    14. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    15. Shota Fujishima, 2015. "The emergence of cooperation through leadership," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 17-36, February.
    16. Burkhard C. Schipper, 2022. "Strategic Teaching and Learning in Games," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 321-352, August.
    17. Ely, Jeffrey & Fudenberg, Drew & Levine, David K., 2008. "When is reputation bad?," Games and Economic Behavior, Elsevier, vol. 63(2), pages 498-526, July.
    18. Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
    19. Sandroni, Alvaro, 2000. "Reciprocity and Cooperation in Repeated Coordination Games: The Principled-Player Approach," Games and Economic Behavior, Elsevier, vol. 32(2), pages 157-182, August.
    20. Hausken, Kjell, 2007. "Reputation, incomplete information, and differences in patience in repeated games with multiple equilibria," Economics Letters, Elsevier, vol. 97(2), pages 138-144, November.

    More about this item

    Keywords

    Repeated Games; Reputation; Equal Discount Factor; Long-run Players; imperfect Observation; Complicated Types; Finite Automaton JEL Classification Numbers: C73; D83;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:nwu:cmsems:1506. 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: Fran Walker (email available below). General contact details of provider: https://edirc.repec.org/data/cmnwuus.html .

    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.