Hotelling competition with multi-purchasing

We analyze a Hotelling model where consumers either buy one out of two goods (single-purchase) or both (multi-purchase). The firms pricing strategies turn out to be fundamentally different if some consumers multi-purchase compared to if all single-purchase. Prices are strategic complements under single-purchase, and increase with quality. In a multi-purchase regime, in contrast, prices are strategically independent because firms then act monopolistically by pricing the incremental benefit to marginal consumers. Furthermore, prices can decrease with quality due to overlapping characteristics. Higher preference heterogeneity increases prices and profits in equilibrium with single-purchase, but decreases them with multi-purchase