Sustainability of collusion and market transparency in a sequential search market: a generalization

The present work generalizes the analytical results of Petrikaite (2016) to a market where more than two firms interact. In other words, we show that, for a generic number of firms in a homogeneous goods market where a continuum of buyers searches sequentially, the relationship between the minimum discount factor which allows the sellers to collude and the share of buyers with null search cost is non-monotonic, reaching a unique interior point of minimum. The first section discusses the motivation of our work and exposes the related literature. The second section summarizes the model of Petrikaite (2016). The third section presents the analytical computations and the mathematical reasoning needed for our generalization, which mainly relies on the Leibniz rule for differentiation under the integral sign and the Bounded Conver­gence Theorem. The fourth section offers policy implications of market design and suggestions for further research.