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Non‐Negative Quantity Constraints and the Duration of Punishment

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  • Luca Lambertini
  • Dan Sasaki

Abstract

In an oligopoly supergame, firms face an obvious technological constraint: the positivity of their production quantities. Applicability of single‐period optimal punishment hinges critically upon the degree of supermodularity in the stage game, as well as upon the positivity constraints on prices and/or quantities. If both prices and quantities are constrained to be positive, then the relevant multi‐period punishment prescribes securitylevel payoffs (where individual rationality binds) when and only when the game is perfectly supermodular, i.e. is either a Bertrand supergame with perfect substitute products or a Cournot supergame with perfect complement products. JEL classification numbers: D43, L13, C72.

Suggested Citation

  • Luca Lambertini & Dan Sasaki, 2002. "Non‐Negative Quantity Constraints and the Duration of Punishment," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 77-93, March.
    • Handle: RePEc:bla:jecrev:v:53:y:2002:i:1:p:77-93
    DOI: 10.1111/1468-5876.00214
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    Cited by:

    1. Robert Gagné & Simon van Norden & Bruno Versaevel, 2003. "Testing Optimal Punishment Mechanisms Under Price Regulation: the Case of the Retail Market for Gasoline," CIRANO Working Papers 2003s-57, CIRANO.
    2. Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2013. "Optimal collusion with limited liability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 203-227, September.
    3. Baldelli, Serena & Lambertini, Luca, 2006. "Price vs quantity in a duopoly supergame with Nash punishments," Research in Economics, Elsevier, vol. 60(3), pages 121-130, September.
    4. Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2009. "Optimal Collusion with Limited Severity Constraint," Working Papers 0909, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    5. Delbono, Flavio & Lambertini, Luca, 2018. "Folk theorems in a class of additively separable games," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 10-15.
    6. F. Delbono & L. Lambertini, 2015. "Parabolic Cylinders and Folk Theorems," Working Papers wp1043, Dipartimento Scienze Economiche, Universita' di Bologna.
    7. F. Delbono & L. Lambertini, 2016. "On Globally Optimal Punishments in the Repeated Cournot Game," Working Papers wp1091, Dipartimento Scienze Economiche, Universita' di Bologna.

    More about this item

    JEL classification:

    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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