Probabilistic Selling for Vertically Differentiated Products in a Decentralized Channel

Problem definition: Probabilistic selling (PS) is a novel selling strategy whereby consumers only know the exact product identity after the payment. By studying PS for vertically differentiated products in a supply chain consisting of one supplier and one retailer, we examine who should assemble the probabilistic products. We explore two cases, retailer assembly (RA) and supplier assembly (SA), analyzing the dynamics and implications within each. Methodology/results: Using game theory methodology, we characterize the best selling strategies for both RA and SA cases, and obtain the equilibrium strategy. Generally, PS is optimal when the associated transaction cost is below a threshold; in this case, PS can alleviate the double marginalization problem in distribution channels. Interestingly, in comparison with a centralized channel, PS adoption is less probable in the RA case but can be more so in the SA case. When PS emerges as the optimal strategy for both cases, the supplier under the SA case mixes a smaller fraction of high-quality products than the retailer would do under the RA case. Moreover, at equilibrium, a relatively powerful supplier should assemble probabilistic products, whereas a relatively powerful retailer may prefer not to have the stewardship of assembling probabilistic products. Notably, PS can serve as a mutually beneficial strategy for the supplier, retailer, and consumers, offering a “win–win–win” outcome. Managerial implications: The supplier should assemble probabilistic products targeting low-type consumers and offer them alongside high-quality (and low-quality) products when the capacity of high-quality products is abundant. Conversely, the supplier should assemble probabilistic products targeting high-type consumers and offer them alongside low-quality products when the capacity of high-quality products is limited. Surprisingly, it may be advantageous for the retailer to delegate the stewardship/assembly of probabilistic products to the supplier, which also benefits the supplier and consumers. PS can create value for all stakeholders by effectively mitigating supply chain inefficiencies.

Funding: X. A. Pan is partially supported by Summer Research Grants awarded by the Warrington College of Business at University of Florida.

Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2024.1036.