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Optimal Punishment in Supergames with Product Differentiation

Author

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  • Lambertini, L.
  • Sasaki, D.

Abstract

We analyse optimal penal codes in both Bertrand and Cournot supergames with product differentiation. We prove that the relationship between optimal punishments and the security level (individually rational discounted profit stream) depends critically on the degree of supermodularity in the stage game, using a duopoly supergame with product differentiation. The security level in the punishment phase is reached only under extreme supermodularity, i.e., when products are perfect substitutes and firms are price setters. Finally, we show that Abreu's rule cannot be implemented under Cournot behaviour and strong demand complementarity between products.

Suggested Citation

  • Lambertini, L. & Sasaki, D., 1998. "Optimal Punishment in Supergames with Product Differentiation," Department of Economics - Working Papers Series 607, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:607
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    Keywords

    GAMES ; PENAL SANCTIONS;

    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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