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 typically assumes abundant inventory and static pricing, often 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, favoring the sale of 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, including mixed bundling, pure bundling, bundle-size pricing, and component pricing. Our analysis reveals that as inventory becomes more constrained relative to market size, the optimal dynamic mixed bundling strategy converges to a dynamic component pricing strategy, 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 reveal that these structural insights extend to policies derived from the standard fluid regime. As the market size grows relative to the inventory, the dynamic mixed bundling policy obtained by resolving the deterministic fluid problem also reduces to a dynamic component pricing policy.