The Comparative Statics of Collusion Models

We develop and illustrate a methodology for obtaining robust comparative statics results for collusion models in markets with differentiated goods by analyzing the homogeneous goods limit of these models. This analysis reveals that the impact of parameter changes on the incentives to deviate from collusion and the punishment profits are often of different order of magnitude yielding comparative statics results that are robust to the functional form of the demand system. We demonstrate with numerical calculations that these limiting results predict the global comparative statics at any degree of product differentiation. We use this methodology to demonstrate the non-robustness of Nash reversion equilibria and to develop new results in the comparative statics of collusion.