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When the Punishment Must Fit the Crime: Remarks on the Failure of Simple Penal Codes in Extensive-Form Games

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  • Mailath, George J.
  • Nocke, Volker
  • White, Lucy

Abstract

In repeated normal-form 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. We provide two examples illustrating that 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

  • 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.
    • Handle: RePEc:cpr:ceprdp:4793
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    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    2. 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..
    3. Rubinstein Ariel & Wolinsky Asher, 1995. "Remarks on Infinitely Repeated Extensive-Form Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 110-115, April.
    4. Sorin Sylvain, 1995. "A Note on Repeated Extensive Games," Games and Economic Behavior, Elsevier, vol. 9(1), pages 116-123, April.
    5. Volker Nocke & Lucy White, 2007. "Do Vertical Mergers Facilitate Upstream Collusion?," American Economic Review, American Economic Association, vol. 97(4), pages 1321-1339, September.
    6. 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.
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    Cited by:

    1. Nocke, Volker & White, Lucy, 2010. "Vertical merger, collusion, and disruptive buyers," International Journal of Industrial Organization, Elsevier, vol. 28(4), pages 350-354, July.
    2. 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.
    3. Salvatore Piccolo & Aldo Pignataro, 2016. "Consumer Loss Aversion, Product Experimentation and Implicit Collusion," CSEF Working Papers 457, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. Escobar, Juan F. & Llanes, Gastón, 2018. "Cooperation dynamics in repeated games of adverse selection," Journal of Economic Theory, Elsevier, vol. 176(C), pages 408-443.
    5. Volker Nocke & Lucy White, 2003. "Do Vertical Mergers Facilitate Upstream Collusion? Second Version," PIER Working Paper Archive 05-013, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 08 Mar 2005.

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    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

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