Managing consumer bracketing purchases: Optimal return policy analysis

Abstract

This paper investigates the optimal pricing and return policies of an online retailer selling a product with multiple versions to consumers facing valuation uncertainty. Consumers resolve their uncertainty through bracketing, a practice wherein they purchase multiple versions with the intention of keeping the best fit and returning the rest. By establishing a Stackelberg game between the retailer and consumers, we investigate two return policies: one offering full refunds with purchase limits, and the other offering partial refunds (Q or R) under exogenous and endogenous pricing (N or P), yielding four scenarios: NQ, PQ, NR, PR. Our study provides key insights into optimal return policies for retailers, demonstrating that stringent return policies may not necessarily be more profitable compared to lenient ones when dealing with consumer bracketing. In the case of exogenous pricing, retailers providing convenient returns are better off charging return fees, while those facing cumbersome returns should offer full refunds under certain conditions. When jointly leveraging pricing, retailers have the flexibility to choose between the full-refund and partial-refund policies. We obtain several interesting findings. First, as the mismatch probability increases, retailers tend to charge higher return fees in Scenario PR, while adjusting optimal decisions (i.e., refund under the partial-refund policy and purchase limit under the full-refund policy) non-monotonically in other scenarios. Second, consumers receive nonnegative expected utility in the exogenous pricing scenario, whereas zero in the endogenous pricing scenario. Third, when returns become sufficiently convenient, retailers adopting the partial-refund policy under endogenous pricing shift toward offering full refunds. In addition, when considering heterogeneous consumers, we discover that in some cases, retailers can benefit from consumer bracketing.