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Non-Negative Quantity Constraints and the Duration of Punishment

Author

Listed:
  • Lambertini, L.
  • Sasaki, D.

Abstract

In an oligopoly supergame, firms face an obvious technological constraint: the positivity of their production quantities. WE show that Lambson's (1987) result on "security-level punishment", that the single-period punishment makes the firm's discounted participation condition just bind, holds only in a Bertrand supergame with perfect substitutes. In general, the sustainability of collusion by means of single-period penal codes hinges critically upon the degree of supermodularity in the stage game, as well as upon the positivity constraints on prices and/or quantities.

Suggested Citation

  • Lambertini, L. & Sasaki, D., 1998. "Non-Negative Quantity Constraints and the Duration of Punishment," Department of Economics - Working Papers Series 630, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:630
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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

    Keywords

    GAMES ; OLIGOPOLIES ; PENAL SANCTIONS;
    All these keywords.

    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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