Sharing Aggregate Inventory Information with Customers: Strategic Cross-Selling and Shortage Reduction

Abstract

This paper studies the strategy of sharing inventory information for a firm that sells two vertically differentiated products. The seller has private information on the aggregate inventory level and the inventory composition between two product variants. The seller credibly and discretionarily discloses inventory information to customers either fully or partially, i.e., disclosing exact inventory of each product variant or the aggregate inventory level. Customers form expectations of future availability and make rational purchasing decisions accordingly. In the disclosure literature, discretion usually leads to the unraveling results: sellers who learn favorable market information opt to disclose it, making full disclosure the equilibrium. This paper shows that aggregate inventory disclosure, i.e., partial disclosure, can be instead sustained as an ex post equilibrium. We demonstrate that inventory information aggregation arises when there is an ex post desire to reduce supply-demand mismatches in all inventory scenarios. Specifically, when customers' preferred products are more likely to stock out, then by withholding product composition but disclosing aggregate inventory level, the seller could entice more incoming consumers who hope that their desired products are in stock. If customers' desired products are sold out, the seller can benefit from up-selling or cross-selling customers' less-preferred products. On the other hand, when the seller stocks more desired products, aggregate disclosure can dampen the flow of incoming customers and reduce the shortage penalty cost. This result is robust under various settings: risk-averse customers, heterogeneous customers, and horizontally-differentiated products.

Keywords: information aggregation, inventory information disclosure, cross-selling, product variety