Sustainability of Collusion and Market Transparency in a Sequential Search Market: a Generalization

TL;DR

This paper extends previous models to analyze how the sustainability of collusion and market transparency behave in markets with more than two firms, revealing a non-monotonic relationship influenced by market information levels.

Contribution

It generalizes existing two-firm models to oligopolies with multiple firms, showing a non-monotonic link between collusion stability and market transparency.

Findings

Critical discount factor varies non-monotonically with informed buyer share.

The relationship between collusion sustainability and market transparency has a unique internal minimum.

Mathematical derivations rely on Leibniz rule and Bounded Convergence Theorem.

Abstract

The present work generalizes the analytical results of Petrikaite (2016) to a market where more than two firms interact. As a consequence, for a generic number of firms in the oligopoly model described by Janssen et al (2005), the relationship between the critical discount factor which sustains the monopoly collusive allocation and the share of perfectly informed buyers is non-monotonic, reaching a unique internal point of minimum. The first section locates the work within the proper economic framework. The second section hosts the analytical computations and the mathematical reasoning needed to derive the desired generalization, which mainly relies on the Leibniz rule for the differentiation under the integral sign and the Bounded Convergence Theorem.