The Diminishing Value of Bundling Under Inventory Scarcity

We study the impact of inventory constraints on bundling in a dynamic pricing setting, challenging the classical view that bundling consistently enhances revenue. Traditional bundling theory, which usually assumes abundant inventory and static pricing settings, typically asserts that bundling generates higher revenue than selling products individually. However, we show that limited inventory, in fact, distorts the revenue extraction capability of bundling in favor of selling the products or services separately. We study the optimal dynamic mixed bundling strategy in a large market regime where the market size grows relative to limited inventory. Leveraging this framework, we derive optimal dynamic pricing policies and value functions for commonly used bundling strategies such as mixed bundling, bundle-size pricing, and bundle-size pricing, in addition to component pricing. Our analysis shows that as inventory becomes more constrained relative to market size, the most general bundling strategy, namely dynamic mixed bundling, converges to a dynamic component pricing approach, outperforming both dynamic bundle-size pricing and dynamic pure bundling. Moreover, the performance gap between these strategies increases with the number of items, a factor typically viewed as favoring bundling when inventory is abundant. Notably, our numerical experiments suggest that these insights also extend to the fluid regime policies, revealing that as the market size increases relative to inventory, the dynamic mixed bundling strategy derived from the fluid regime mimics a dynamic component pricing strategy.