Dynamic Pricing Strategies with Reference Effects

The authors consider the dynamic pricing problem of a monopolistic firm in a market with repeated interactions, where demand is sensitive to the firm's pricing history. Consumers have memory and are prone to human decision making biases and cognitive limitations. As the firm manipulates prices, consumers form a reference price that adjusts as an anchoring standard based on price perceptions. Purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price, in the spirit of prospect theory. The authors prove that optimal pricing policies induce a perception of monotonic prices, whereby consumers always perceive a discount, or surcharge, relative to their expectations. The effect is that of a skimming or penetration strategy. In the long term, the firm's optimal pricing path is eventually monotonic. The authors identify conditions where this is also true at the introductory stage. If consumers are loss averse, the authors show that optimal prices converge to a constant steady state price, characterized by a simple implicit equation; in other words, the optimal policy cycles. The range of steady state price is unique for loss neutral buyers, and decreases with the strength of the reference effect, and with customer's memory, all else equal. Offering lower prices to frequent customers may be suboptimal, however, if they are less sensitive to price changes than occasional buyers. If managers ignore such long-term implications of their pricing strategy, the model indicates that they will systematically price too low and lose revenue. These results hold under very general reference dependent demand models.