IDEAS home Printed from https://ideas.repec.org/p/pen/papers/15-008.html
   My bibliography  Save this paper

When and How the Punishment Must Fit the Crime

Author

Listed:
  • George J.Mailath

    (Department of Economics and PIER, University of Pennsylvania, and Research School of Economics, Australian National University)

  • Volker Nocke

    (University of Mannheim, CESifo and CEPR)

  • Lucy White

    (Harvard Business School and CEPR)

Abstract

In repeated normal-form (simultaneous-move) games, simple penal codes (Abreu, 1986, 1988) permit an elegant characterization of the set of subgame-perfect outcomes. We show that the logic of simple penal codes fails in repeated extensive-form games. By means of examples, we identify two types of settings in which a subgame-perfect outcome may be supported only by a profile with the property that the continuation play after a deviation is tailored not only to the identity of the deviator, but also to the nature of the deviation.

Suggested Citation

  • George J.Mailath & Volker Nocke & Lucy White, 2015. "When and How the Punishment Must Fit the Crime," PIER Working Paper Archive 15-008, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  • Handle: RePEc:pen:papers:15-008
    as

    Download full text from publisher

    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/15-008.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Susan Athey & Andrew Atkeson & Patrick J. Kehoe, 2005. "The Optimal Degree of Discretion in Monetary Policy," Econometrica, Econometric Society, vol. 73(5), pages 1431-1475, September.
    2. Jonathan Levin, 2003. "Relational Incentive Contracts," American Economic Review, American Economic Association, vol. 93(3), pages 835-857, June.
    3. Baron, David P. & Ferejohn, John A., 1989. "Bargaining in Legislatures," American Political Science Review, Cambridge University Press, vol. 83(4), pages 1181-1206, December.
    4. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    5. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Econometrica, Econometric Society, vol. 65(6), pages 1467-1478, November.
    6. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    7. Rasmusen, Eric B & Ramseyer, J Mark & Wiley, John S, Jr, 1991. "Naked Exclusion," American Economic Review, American Economic Association, vol. 81(5), pages 1137-1145, December.
    8. Grossman, Sanford J & Hart, Oliver D, 1986. "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 691-719, August.
    9. Timothy N. Cason & Vai‐Lam Mui, 2014. "Coordinating Resistance Through Communication and Repeated Interaction," Economic Journal, Royal Economic Society, vol. 124(574), pages 226-256, February.
    10. Drew Fudenberg & Eric Maskin, 2008. "The Folk Theorem In Repeated Games With Discounting Or With Incomplete Information," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 11, pages 209-230, World Scientific Publishing Co. Pte. Ltd..
    11. Weingast, Barry R., 1997. "The Political Foundations of Democracy and the Rule of the Law," American Political Science Review, Cambridge University Press, vol. 91(2), pages 245-263, June.
    12. Rubinstein Ariel & Wolinsky Asher, 1995. "Remarks on Infinitely Repeated Extensive-Form Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 110-115, April.
    13. Sorin Sylvain, 1995. "A Note on Repeated Extensive Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 116-123, April.
    14. Volker Nocke & Lucy White, 2007. "Do Vertical Mergers Facilitate Upstream Collusion?," American Economic Review, American Economic Association, vol. 97(4), pages 1321-1339, September.
    15. Quan Wen, 2002. "A Folk Theorem for Repeated Sequential Games," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(2), pages 493-512.
    16. Klein, Benjamin & Crawford, Robert G & Alchian, Armen A, 1978. "Vertical Integration, Appropriable Rents, and the Competitive Contracting Process," Journal of Law and Economics, University of Chicago Press, vol. 21(2), pages 297-326, October.
    17. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1990. "Toward a Theory of Discounted Repeated Games with Imperfect Monitoring," Econometrica, Econometric Society, vol. 58(5), pages 1041-1063, September.
    18. Weingast, Barry R, 1995. "The Economic Role of Political Institutions: Market-Preserving Federalism and Economic Development," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 11(1), pages 1-31, April.
    19. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    20. Mailath, George J. & Samuelson, Larry, 2006. "Repeated Games and Reputations: Long-Run Relationships," OUP Catalogue, Oxford University Press, number 9780195300796.
    21. John Sutton, 1986. "Non-Cooperative Bargaining Theory: An Introduction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(5), pages 709-724.
    22. Michael D. Whinston & Ilya R. Segal, 2000. "Naked Exclusion: Comment," American Economic Review, American Economic Association, vol. 90(1), pages 296-309, March.
    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. Biancini, Sara & Ettinger, David, 2017. "Vertical integration and downstream collusion," International Journal of Industrial Organization, Elsevier, vol. 53(C), pages 99-113.
    2. Emilio Bisetti & Benjamin Tengelsen & Ariel Zetlin‐Jones, 2022. "Moral Hazard In Remote Teams," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(4), pages 1595-1623, November.
    3. Isabel Strecker, 2024. "Gambling bank behaviour, incentive mechanism, and sanctions: A two-stage model," Journal of Banking Regulation, Palgrave Macmillan, vol. 25(2), pages 197-208, June.
    4. Sebastian Schweighofer-Kodritsch, 2015. "Time Preferences and Bargaining," STICERD - Theoretical Economics Paper Series /2015/568, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

    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. Stefan Buehler & Dennis L. Gärtner, 2013. "Making Sense of Nonbinding Retail-Price Recommendations," American Economic Review, American Economic Association, vol. 103(1), pages 335-359, February.
    2. 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.
    3. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    4. Liu, Ce & Ali, S. Nageeb, 2019. "Conventions and Coalitions in Repeated Games," Working Papers 2019-8, Michigan State University, Department of Economics.
    5. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    6. Labrecciosa Paola & Colombo Luca, 2010. "Technology Uncertainty and Market Collusion," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 10(1), pages 1-17, March.
    7. Spagnolo, Giancarlo, 2005. "Managerial incentives and collusive behavior," European Economic Review, Elsevier, vol. 49(6), pages 1501-1523, August.
    8. Mailath, George J. & Nocke, Volker & White, Lucy, 2004. "When the Punishment Must Fit the Crime: Remarks on the Failure of Simple Penal Codes in Extensive-Form Games," CEPR Discussion Papers 4793, C.E.P.R. Discussion Papers.
    9. Sugaya, Takuo & Wolitzky, Alexander, 2018. "Bounding payoffs in repeated games with private monitoring: n-player games," Journal of Economic Theory, Elsevier, vol. 175(C), pages 58-87.
    10. Samuelson, Larry & Stacchetti, Ennio, 2017. "Even up: Maintaining relationships," Journal of Economic Theory, Elsevier, vol. 169(C), pages 170-217.
    11. Bart S. Vanneste & Douglas H. Frank, 2014. "Forgiveness in Vertical Relationships: Incentive and Termination Effects," Organization Science, INFORMS, vol. 25(6), pages 1807-1822, December.
    12. Christian A. Ruzzier, 2009. "Asset Specificity and Vertical Integration: Williamson’s Hypothesis Reconsidered," Harvard Business School Working Papers 09-119, Harvard Business School.
    13. Goldlücke, Susanne & Kranz, Sebastian, 2012. "Infinitely repeated games with public monitoring and monetary transfers," Journal of Economic Theory, Elsevier, vol. 147(3), pages 1191-1221.
    14. Opp, Marcus M., 2010. "Tariff wars in the Ricardian Model with a continuum of goods," Journal of International Economics, Elsevier, vol. 80(2), pages 212-225, March.
    15. Kolotilin, Anton & Li, Hongyi, 2021. "Relational communication," Theoretical Economics, Econometric Society, vol. 16(4), November.
    16. Kimmo Berg & Markus Kärki, 2018. "Critical Discount Factor Values in Discounted Supergames," Games, MDPI, vol. 9(3), pages 1-17, July.
    17. Etro, Federico, 2016. "Research in economics and industrial organization," Research in Economics, Elsevier, vol. 70(4), pages 511-517.
    18. Ansink, Erik & Houba, Harold, 2016. "Sustainable agreements on stochastic river flow," Resource and Energy Economics, Elsevier, vol. 44(C), pages 92-117.
    19. Etro, Federico, 2017. "Research in economics and game theory. A 70th anniversary," Research in Economics, Elsevier, vol. 71(1), pages 1-7.
    20. Takashi Kamihigashi & Taiji Furusawa, 2007. "Global Dynamics in Infinitely Repeated Games with Additively Separable Continuous Payoffs," Discussion Paper Series 210, Research Institute for Economics & Business Administration, Kobe University.

    More about this item

    Keywords

    Simple Penal Code; Subgame Perfect Equilibrium; Repeated Extensive Game; Optimal Punishment.;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • 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

    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:pen:papers:15-008. 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: Administrator (email available below). General contact details of provider: https://edirc.repec.org/data/deupaus.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.