Cournot platform competition with mixed-homing

Competition in quantity dates back to Cournot (1838) for traditional markets and Katz and Shapiro (1985) for markets with direct network effects. In this paper, we consider Cournot platform competition in two-sided markets with indirect network effects while allowing for single-, multi-, and mixed-homing allocations. We find that the markup and markdown terms that are typically found in monopoly two-sided pricing are distorted toward zero when platform competition intensifies. We also generalize the monopoly platform Lerner indices from Armstrong (2006) and Weyl (2010) to include competition and mixed-homing allocations. Lastly, we show that welfare decreases in the number of platforms for the most commonly considered homing allocations, highlighting how the welfare loss from breaking up a network across smaller platforms can outweigh the welfare benefits from lower aggregate prices in a setting where platforms are homogenous.