Robust Pricing in Discrete Time

We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a discrete number of periods. Customers are heterogeneous in both the willingness-to-pay for the product and the arrival time during the selling season. We assume that the seller knows only the support of the customers’ valuations and do not make any other distributional assumptions about customers’ willingnessto-pay or arrival times. In this setting, we consider a robust formulation of the seller’s pricing problem which is based on the minimization of her worst-case regret. This regret is defined as the difference between her payoff under full demand information and her realized payoff. We consider two distinct cases of customers’ purchasing behavior: myopic and strategic customers. For each of these demand models, we characterize the optimal pricing strategy and corresponding minimum regret. We also derive a continuous-time pricing approximation as the limit of the discrete-time model when the length of the periods decreases to zero. A continuous-time model has been considered in Caldentey et al. (2015). Interestingly, in the limit, the pricing strategy of the discrete model presents a different structural property from the strategy presented in Caldentey et al. (2015), which leads to a set of different managerial insights for the firm.