Antitrust & Competition Policy Blog

Editor: D. Daniel Sokol
University of Florida
Levin College of Law

A Member of the Law Professor Blogs Network

Tuesday, February 16, 2010

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

Posted by D. Daniel Sokol

Paul Zimmerman (FTC) provides his thoughts On the sustainability of collusion in Bertrand supergames with discrete pricing and nonlinear demand.

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 th! e 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.

http://lawprofessors.typepad.com/antitrustprof_blog/2010/02/on-the-sustainability-of-collusion-in-bertrand-supergames-with-discrete-pricing-and-nonlinear-demand.html

| Permalink

TrackBack URL for this entry:

http://www.typepad.com/services/trackback/6a00d8341bfae553ef012877763f36970c

Listed below are links to weblogs that reference On the sustainability of collusion in Bertrand supergames with discrete pricing and nonlinear demand :

Comments

Post a comment