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

Zimmerman, Paul R. (2010): On the sustainability of collusion in Bertrand supergames with discrete pricing and nonlinear demand. Unpublished.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bertrand supergames; cartels; collusion sustainability; discrete pricing; nonlinear demand
• Subjects: L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets; L - Industrial Organization > L4 - Antitrust Issues and Policies > L41 - Monopolization; Horizontal Anticompetitive Practices

References

Alperovich, G. and I. Weksler (1996), A class of utility functions yielding linear demand functions, American Economist 40: 20-23.

Benson, B.L. (1980), Löschian competition under alternative demand conditions, American Economic Review 70: 1098-1105.

Collie, D. (2004), Collusion and the elasticity of demand, Economics Bulletin 12: 1-6.

Coughlin, P.J. (1984), Changes in marginal revenue and related elasticities, Southern Economic Journal 51: 568-573.

Deneckere. R. (1983), Duopoly supergames with product differentiation, Economics Letters 11: 37-42.

Formby, J.P., S. Layson, and W.J. Smith (1982), The law of demand, positive sloping marginal revenue, and multiple profit equilibrium, Economic Inquiry 20: 303-311.

Friedman, J.W. (1971), A non-cooperative equilibrium for supergames, Review of Economic Studies 38: 1-12.

Gallice, A. (2008), The neglected effects of demand characteristics on the sustainability of collusion, CEPR Discussion Paper No. 6975.

Hayrapetyan, A., É. Tados, and T. Wexler (2007), A network pricing game for selfish traffic, Distributed Computing 19: 255-262.

Lambertini, L. (1996), Cartel stability and the curvature of market demand, Bulletin of Economic Research 48: 329-334.

Levenstein, M.C. and V.Y. Suslow (2006), What determines cartel success?, Journal of Economic Literature 44: 43-95.

Rothschild, R. (1992), On the sustainability of collusion in differentiated duopolies, Economics Letters 40: 33-37.

Singh, N. and X. Vives (1984), Price and quantity competition in a differentiated duopoly, Rand Journal of Economics 10: 20-32.

Tyagi, R.K. (1999), On the relationship between product substitutability and tacit collusion, Managerial and Decision Economics 20: 293-298.

Walters, A.A. (1980), A note on monopoly equilibrium, Economic Journal 90: 161-162.