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On the sustainability of collusion in Bertrand supergames with discrete pricing and nonlinear demand

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  • Zimmerman, Paul R.

Abstract

In traditional industrial organization models of Bertrand supergames, the critical discount factor governing the sustainability of collusion is independent of key demand and supply parameters. Recent research has demonstrated that these counterintuitive results stem from the assumption that firms can change prices in infinitesimally small increments (i.e., continuously). This note considers the effects of demand curvature in the context of a model of collusion where, as in Gallice (2008), Bertrand competitors can deviate only by lowering prices by some small, discrete amount. Two alternative demand specifications that capture the influence of demand curvature are considered. In either case, it is shown that with discrete price changes the critical discount factor is determined by the key demand parameters, including demand curvature. However, the direct effects of increased concavity (or convexity) in market demand on the sustainability of collusion runs in opposite directions across the two models. This discrepancy is shown to arise from the way in which the respective demand curves rotate in response to a change in the demand curvature parameter. The results support the conclusion of earlier research that determining the potential for collusion in homogenous goods industries likely requires careful case-by-case investigation.

Suggested Citation

  • Zimmerman, Paul R., 2010. "On the sustainability of collusion in Bertrand supergames with discrete pricing and nonlinear demand," MPRA Paper 20249, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:20249
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    File URL: https://mpra.ub.uni-muenchen.de/20249/1/MPRA_paper_20249.pdf
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    References listed on IDEAS

    as
    1. Lambertini, Luca, 1996. "Cartel Stability and the Curvature of Market Demand," Bulletin of Economic Research, Wiley Blackwell, vol. 48(4), pages 329-334, October.
    2. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    3. Rothschild, R., 1992. "On the sustainability of collusion in differentiated duopolies," Economics Letters, Elsevier, vol. 40(1), pages 33-37, September.
    4. Gallice, Andrea, 2010. "The neglected effects of demand characteristics on the sustainability of collusion," Research in Economics, Elsevier, vol. 64(4), pages 240-246, December.
    5. Formby, John P & Layson, Stephen & Smith, W James, 1982. "The Law of Demand, Positive Sloping Marginal Revenue, and Multiple Profit Equilibria," Economic Inquiry, Western Economic Association International, vol. 20(2), pages 303-311, April.
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    7. Walters, A A, 1980. "A Note on Monopoly Equilibrium," Economic Journal, Royal Economic Society, vol. 90(357), pages 161-162, March.
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    9. repec:ebl:ecbull:v:12:y:2004:i:3:p:1-6 is not listed on IDEAS
    10. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
    11. David Collie, 2004. "Collusion and the elasticity of demand," Economics Bulletin, AccessEcon, vol. 12(3), pages 1-6.
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    More about this item

    Keywords

    Bertrand supergames; cartels; collusion sustainability; discrete pricing; nonlinear demand;

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices

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