Dynamic pricing when consumers are strategic: Analysis of a posted pricing scheme

We study dynamic pricing policies for a monopolist selling perishable products over a finite time horizon to buyers who are strategic. Buyers are strategic in the sense that they anticipate the firm’s pricing policies. We are interested in situations in which auctions are not feasible and in which it is costly to change prices. We begin by showing that unless strategic buyers expect shortages dynamic pricing will not increase revenues. We investigate two pricing schemes that we call posted and contingent pricing. In the posted pricing scheme at the beginning of the horizon the firm announces a set of prices. In the contingent pricing scheme price evolution depends upon demand realization. Our focus is on the posted pricing scheme because of its ease of implementation. In equilibrium, buyers will employ a threshold policy in both pricing regimes i.e., they will buy only if their private valuations are above a particular threshold. We show that a multi-unit auction with a reservation price provides an upper bound for the expected revenues for both pricing schemes. Numerical examples suggest that a posted pricing scheme with two or three price changes is enough to achieve revenues that are close to the upper bound. Counter to intuition we find that neither a posted pricing scheme nor a contingent pricing scheme is dominant. The difference in expected revenues of these two schemes is small. We also investigate whether or not it is optimal for the seller to conceal inventory and sales information from buyers. A firm benefits if it reveals the number of units it has for sale and subsequently withholds information about the number of units sold at different prices.