Abstract
Subscriptions increasingly put repeat purchases on “autopilot,” while pay-as-you-go retail keeps shoppers free to compare prices and switch. As more firms try to offer both formats, a core question for operations and strategy is when a hybrid menu is a profitable segmentation lever and when it backfires through cannibalization and tougher rivalry. We study a duopoly selling a frequently repurchased product over many seasons. Firms choose a selling format (subscription, retail, or hybrid) and commit to long-run profit margins while procurement costs fluctuate over time. Consumers are two-dimensionally heterogeneous: they differ in preferred seller (horizontal fit) and in search frictions, which generate endogenous sorting between lock-in and switching.
Equilibrium exhibits a sharp threshold pattern in cost volatility. The hybrid model is not universally superior; it creates value only under moderate volatility by segmenting “convenience seekers” from “bargain hunters.” We derive two counterintuitive insights that challenge conventional wisdom. First, search frictions and cost volatility act as substitutes: higher search costs do not always strengthen the case for lock-in when procurement costs fluctuate substantially. Second, competitive effects are non-monotone: adding a subscription option can soften price competition via segmentation, while greater differentiation or higher search frictions can intensify rivalry by shifting the equilibrium format. Finally, we show that symmetric hybrid adoption can generate a unique win–win region that increases both firm profits and consumer surplus.