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Optimal Punishments in Supergames With Close Substitutes

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  • L. Lambertini
  • D. Sasaki

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 linear 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

  • L. Lambertini & D. Sasaki, 1997. "Optimal Punishments in Supergames With Close Substitutes," Working Papers 304, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:304
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    References listed on IDEAS

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    1. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
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    3. Chang, Myong-Hun, 1992. "Intertemporal Product Choice and Its Effects on Collusive Firm Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 773-793, November.
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