Markovian pricing with price guarantees

Abstract

A stream of recent research considers the practice of random price discounts (a.k.a randomized pricing) when selling to forward-looking customers and shows that such pricing strategies can mitigate strategic customer waiting and boost seller profit. In practice, random price discounts are often offered together with price guarantees, in which customers are refunded the price difference if the price is lowered within a given time window after purchase. This paper investigates the efficacy of price guarantees under randomized pricing. To that end, we consider a model in which a firm adopts Markovian pricing and interacts with customers over an infinite time horizon. The following results are obtained. First, while Markovian pricing allows firms to price discriminate customers based on their monitoring costs, price guarantees further allow firms to price discriminate customers based on their willingness to pay. Second, offering price guarantees under Markovian pricing can help retain customers effectively by inducing high-valuation customers to purchase early, regardless of their arrival time. Third, even with price guarantees, Markovian pricing can dominate static pricing only when high-valuation customers are more likely to have a high monitoring cost, which illustrates that customer composition plays a crucial role in the effectiveness of the firm’s pricing strategy. Fourth, the optimal duration of price guarantees is closely related to customers’ lifetime duration. Finally, perhaps surprisingly, offering price guarantees can decrease the aggregate customer surplus since the firm offers sale prices less often under price guarantees.