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Reputation with Analogical Reasoning

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  • Philippe Jehiel
  • Larry Samuelson

Abstract

We consider a repeated interaction between a long-run player and a sequence of short-run players, in which the long-run player may either be rational or may be a mechanical type who plays the same (possibly mixed) action in every stage game. We depart from the classical model in assuming that the short-run players make inferences by analogical reasoning, meaning that they correctly identify the average strategy of each type of long-run player, but do not recognize how this play varies across histories. Concentrating on 2 × 2 games, we provide a characterization of equilibrium payoffs, establishing a payoff bound for the rational long-run player that can be strictly larger than the familiar "Stackelberg" bound. We also provide a characterization of equilibrium behavior, showing that play begins with either a reputation-building or a reputation-spending stage (depending on parameters), followed by a reputation-manipulation stage. Copyright 2012, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:qjecon:v:127:y:2012:i:4:p:1927-1969
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    File URL: http://hdl.handle.net/10.1093/qje/qjs031
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    References listed on IDEAS

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    1. David Ettinger & Philippe Jehiel, 2010. "A Theory of Deception," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 1-20, February.
    2. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
    3. Cripps, Martin W. & Mailath, George J. & Samuelson, Larry, 2007. "Disappearing private reputations in long-run relationships," Journal of Economic Theory, Elsevier, vol. 134(1), pages 287-316, May.
    4. George J. Mailath & Larry Samuelson, 2001. "Who Wants a Good Reputation?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 415-441.
    5. 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..
    6. Martin W. Cripps & George J. Mailath & Larry Samuelson, 2004. "Imperfect Monitoring and Impermanent Reputations," Econometrica, Econometric Society, vol. 72(2), pages 407-432, March.
    7. David Ettinger & Philippe Jehiel, 2010. "A Theory of Deception," American Economic Journal: Microeconomics, American Economic Association, vol. 2(1), pages 1-20, February.
    8. Liu, Qingmin & Skrzypacz, Andrzej, 2009. "Limited Records and Reputation," Research Papers 2030, Stanford University, Graduate School of Business.
    9. Kreps, David M. & Wilson, Robert, 1982. "Reputation and imperfect information," Journal of Economic Theory, Elsevier, vol. 27(2), pages 253-279, August.
    10. repec:dau:papers:123456789/5434 is not listed on IDEAS
    11. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    12. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
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    Cited by:

    1. David Ettinger & Philippe Jehiel, 2021. "An experiment on deception, reputation and trust," Experimental Economics, Springer;Economic Science Association, vol. 24(3), pages 821-853, September.
    2. Jehiel, Philippe & Samuelson, Larry, 2023. "The analogical foundations of cooperation," Journal of Economic Theory, Elsevier, vol. 208(C).
    3. Jehiel, Philippe, 2015. "Investment strategy and selection bias: An equilibrium perspective on overconfidence," CEPR Discussion Papers 10868, C.E.P.R. Discussion Papers.
    4. Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    5. Philippe Jehiel, 2022. "Analogy-Based Expectation Equilibrium and Related Concepts:Theory, Applications, and Beyond," Working Papers halshs-03735680, HAL.
    6. Bilancini, Ennio & Boncinelli, Leonardo, 2018. "Signaling to analogical reasoners who can acquire costly information," Games and Economic Behavior, Elsevier, vol. 110(C), pages 50-57.
    7. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
    8. Harry Pei, 2020. "Reputation for Playing Mixed Actions: A Characterization Theorem," Papers 2006.16206, arXiv.org, revised Apr 2021.
    9. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    10. Andrew Mell, 2015. "Fooling Some of the People Some of the Time: Reputation Management and Optimal Betrayal," Economics Series Working Papers 770, University of Oxford, Department of Economics.
    11. Alessandro Pavan, 2014. "Attention, Coordination, and Bounded Recall," Discussion Papers 1576, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    13. Yingkai Li & Harry Pei, 2020. "Misspecified Beliefs about Time Lags," Papers 2012.07238, arXiv.org.
    14. Paul E. Fischer & Mirko S. Heinle & Kevin C. Smith, 2020. "Constrained listening, audience alignment, and expert communication," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 1037-1062, December.
    15. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.

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