Contingent Preannounced Pricing Policies with Strategic Consumers

Companies in diverse industries must decide the pricing policy of their inventories over time. This decision becomes particularly complex when customers are forward looking and may defer a purchase in the hope of future discounts and promotions. With such uncertainty, many customers may end up not buying or buying at a significantly lower price, reducing the firm's profitability. Recent studies show that a way to mitigate this negative effect caused by strategic consumers is to use a posted or preannounced pricing policy. With that policy, firms commit to a price path that consumers use to evaluate their purchase timing decision. In this paper, we propose a class of preannounced pricing policies in which the price path corresponds to a price menu contingent on the available inventory. We present a two-period model, with a monopolist selling a fixed inventory of a good. Given a menu of prices specified by the firm and beliefs regarding the number of units to be sold, customers decide whether to buy upon arrival, buy at the clearance price, or not to buy. The firm determines the set of prices that maximizes revenues. The solution to this problem requires the concept of equilibrium between the seller and the buyers that we analyze using a novel approach based on ordinary differential equations. We show existence of equilibrium and uniqueness when only one unit is on sale. However, if multiple units are offered, we show that multiple equilibria may arise. We develop a gradient-based method to solve the firm's optimization problem and conduct a computational study of different pricing schemes. The results show that under certain conditions the proposed contingent preannounced policy outperforms previously proposed pricing schemes. The source of the improvement comes from the use of the proposed pricing policy as a barrier to discourage strategic waiting and as a discrimination tool for those customers waiting.