Skip to main content

Optimal punishments in linear duopoly supergames with product differentiation

Abstract

We analyze 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 behavior and strong demand complementarity between products.

This is a preview of subscription content, access via your institution.

References

  1. Abreu, D. J. (1986): “Extremal Equilibria of Oligopolistic Supergames.”Journal of Economic Theory 39: 191–225.

    Google Scholar 

  2. — (1988): “On the Theory of Infinitely Repeated Games with Discounting.”Econometrica 56: 383–396.

    Google Scholar 

  3. Bulow, J., Geanakoplos, J., and Klemperer, P. (1985): “Multimarket Oligopoly: Strategic Substitutes and Complements.”Journal of Political Economy 93: 488–511.

    Google Scholar 

  4. Chang, M. H. (1991): “The Effects of Product Differentiation on Collusive Pricing.”International Journal of Industrial Organization 9: 453–469.

    Google Scholar 

  5. — (1992): “Intertemporal Product Choice and Its Effects on Collusive Firm Behavior.”International Economic Review 33: 773–793.

    Google Scholar 

  6. Deneckere, R. (1983): “Duopoly Supergames with Product Differentiation.”Economics Letters 11: 37–42.

    Google Scholar 

  7. — (1984): “Corrigenda.”Economics Letters 15: 385–387.

    Google Scholar 

  8. Dixit, A. K. (1979): “A Model of Duopoly Suggesting a Theory of Entry Barriers.”Bell Journal of Economics 10: 20–32.

    Google Scholar 

  9. Friedman, J. W. (1971): “A Non-Cooperative Equlibrium for Supergames.”Review of Economic Studies 28: 1–12.

    Google Scholar 

  10. Friedman, J. W., and Thisse, J.-F. (1993): “Partial Collusion Fosters Minimum Product Differentiation.”Rand Journal of Economics 24: 631–645.

    Google Scholar 

  11. Fudenberg, D., and Tirole, J. (1991):Game Theory. Cambridge, Mass.: MIT Press.

    Google Scholar 

  12. Häckner, J. (1994): “Collusive Pricing in Markets for Vertically Differentiated Products.”International Journal of Industrial Organization 12: 155–177.

    Google Scholar 

  13. — (1995): “Endogenous Product Design in an Infinitely Repeated Game.”International Journal of Industrial Organization 13: 277–299.

    Google Scholar 

  14. — (1996): “Optimal Symmetric Punishments in a Bertrand Differentiated Products Duopoly.”International Journal of Industrial Organization 14: 611–630.

    Google Scholar 

  15. Lambertini, L. (1997): “Prisoners' Dilemma in Duopoly (Super)Games.”Journal of Economic Theory 77: 181–191.

    Google Scholar 

  16. Lambson, V. E. (1987): “Optimal Penal Codes in Price-Setting Supergames with Capacity Constraints.”Review of Economic Studies 54: 385–397.

    Google Scholar 

  17. — (1994): “Some Results on Optimal Penal Codes in Asymmetric Bertrand Supergames.”Journal of Economic Theory 62: 444–468.

    Google Scholar 

  18. — (1995): “Optimal Penal Codes in Nearly Symmetric Bertrand Supergames with Capacity Constraints.”Journal of Mathematical Economics 24: 1–22.

    Google Scholar 

  19. Ross, T. W. (1992): “Cartel Stability and Product Differentiation.”International Journal of Industrial Organization 10: 1–13.

    Google Scholar 

  20. Rothschild, R. (1992): “On the Sustainability of Collusion in Differentiated Duopolies.”Economics Letters 40: 33–37.

    Google Scholar 

  21. Singh, N., and Vives, X. (1984): “Price and Quantity Competition in a Differentiated Duopoly.”Rand Journal of Economics 15: 546–554.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Lambertini, L., Sasaki, D. Optimal punishments in linear duopoly supergames with product differentiation. Zeitschr. f. National#x00F6;konomie 69, 173–188 (1999). https://doi.org/10.1007/BF01232420

Download citation

Keywords

  • penal codes
  • security level
  • product differentiation
  • positivity constraints

JEL classification

  • C72
  • D43
  • L13