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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 20249.

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Date of creation: 25 Jan 2010
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Handle: RePEc:pra:mprapa:20249

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

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  1. 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.
  2. David Collie, 2004. "Collusion and the elasticity of demand," Economics Bulletin, AccessEcon, vol. 12(3), pages 1-6.
  3. Benson, Bruce L, 1980. "Loschian Competition under Alternative Demand Conditions," American Economic Review, American Economic Association, vol. 70(5), pages 1098-1105, December.
  4. Luca Lambertini, 1994. "Cartel Stability and the Curvature of Market Demand," Working Papers 211, Dipartimento Scienze Economiche, Universita' di Bologna.
  5. Rothschild, R., 1992. "On the sustainability of collusion in differentiated duopolies," Economics Letters, Elsevier, vol. 40(1), pages 33-37, September.
  6. Deneckere, R., 1983. "Duopoly supergames with product differentiation," Economics Letters, Elsevier, vol. 11(1-2), pages 37-42.
  7. 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 303-11, April.
  8. Rajeev K. Tyagi, 1999. "On the relationship between product substitutability and tacit collusion," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 20(6), pages 293-298.
  9. Walters, A A, 1980. "A Note on Monopoly Equilibrium," Economic Journal, Royal Economic Society, vol. 90(357), pages 161-62, March.
  10. repec:ebl:ecbull:v:12:y:2004:i:3:p:1-6 is not listed on IDEAS
  11. Friedman, James W, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Wiley Blackwell, vol. 38(113), pages 1-12, January.
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