Platform Competition with Multihoming on Both Sides: Subsidize or Not?

As the costs of joining platforms decrease, we often see participants in both sides of two-sided platforms to multihome, a case mostly ignored in the literature on competition between two-sided platforms. We help to 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 multihome. We show that in that case the strategic interdependence between the two sides of the same platform may be of lesser importance, or even not be present at all, compared to models that assume single-homing on at least one side of the market. The implication is that when multihoming may be present on both sides of the market, the benefit of subsidizing one side (typically the one with higher price elasticity) is diminished or may not be present at all. This outcome differs from most of the two-sided platform literature, where interdependence between the two sides served by the same platform is a major result leading to the policy implication that a platform will often maximize its total profits by subsidizing one side, typically the one with more elastic demand. Our analysis shows that the common strategic advice to subsidize one side in order to maximize total profits may be limited or even incorrect when both sides multihome, which can be significant given the increasing prevalence of multihoming.