Platform Competition with Multi-Homing on Both Sides: Subsidize or Not?

A major result in the study of two-sided platforms is the strategic interdependence between the two sides of the same platform, leading to the implication that a platform can maximize its total profits by subsidizing one of its sides. We show that this result largely depends on assuming that at least one side of the market single-homes. As technology makes joining multiple platforms easier, we increasingly observe that participants on both sides of two-sided platforms multi-home. The case of multi-homing on both sides is mostly ignored in the literature on competition between two-sided platforms. We help fill this gap by developing a model for platform competition in a differentiated setting (a Hoteling line), which is similar to other models in the literature but focuses on the case where at least some agents on each side multi-home. We show that when both sides in a platform market multi-home, the strategic interdependence between the two sides of the same platform will diminish or even disappear. Our analysis suggests that the common strategic advice to subsidize one side in order to maximize total profits may be limited or even incorrect when both sides multi-home, which is an important caveat given the increasing prevalence of multi-homing in platform markets.