Optimal pricing of a duopoly platform with two-sided congestion effect

We study in this paper the impact of two-sided congestion effect on the pricing policy of a two-sided duopoly. Relative to the benchmark framework of Armstrong (2006), we show that with congestion effect the "divide and conquer" pricing strategy is reduced and therefore competition for submarket share is softened. The major issue we notice in this paper is that with congestion effect, each platform charges any type a price that covers not only the marginal congestion cost such an agent imposes on another of-same-type having joined its platform but also it covers the marginal congestion cost that he indirectly imposes on any of-same-type agent being chosen to join the rival platform. The reason behind this is linked to the fact that each agent frequenting one platform urges some of-same-type agents to access to the rival platform.