Abstract
Existing models of price competition in the presence of endogenous consumer search restrict attention to single-brand firms, ensuring that any consumer who receives multiple price quotes places firms in competition with each other. We extend these models to allow a single firm to own two brands, meaning that a consumer who receives exactly two price quotes may receive two from the same firm, and hence be "captive" to that firm. If there are sufficiently many such consumers, requiring two merging firms to consolidate their brands rather than operate them separately would increase competition and benefit consumers. Similarly, curtailing brand proliferation by restricting firms from introducing multiple brands for the same product or limiting the visibility of such duplicate brands on online platforms can intensify price competition and benefit consumers. These results are also true if consumers operate under an "illusion of competition" in which they are unaware that separate brands may be co-owned by the same firm, believing them all to be independent competitors. Breaking such an illusion of competition by advertising the brand ownership structure may help or hurt consumers.