Selling to Heterogeneous Strategic Customers with Uncertain Valuations under Returns Policies

We consider a firm selling a fixed amount of inventory to customers who possess uncertain valuations on a product prior to purchase and realize their complete valuations only after purchase. The firm determines the returns policies over two periods; each of which targets for a group of brand loyal customers or regular shoppers. The customers are strategic, taking into account both the product availability risk and the product misfit risk when they decide when to purchase. We identify two effects of returns including the positive effect of delay mitigation and the negative effect of surplus reduction, resulting in no returns to brand loyal customers in the first period and a positive refund to regular shoppers in the second period. The result complements Su (2009)’s finding returns itself is not beneficial for the firm when faced with homogeneous customers with uncertain valuations. However, when customers have distinct and uncertain valuations, returns offered in a later period mitigates the incentive of loyal customers to delay their purchases. Hence, returns provides the firm with an additional instrument to mitigate the negative consequences of strategic customer behavior. We find that, with returns, the markup can emerge as the optimal pricing policy when the firm holds a high inventory. We also investigate how the benefit of returns over no returns is affected by the firm’s initial inventory level and customer valuation uncertainty.