Dynamic Pricing Strategies with Reference Effects

Abstract

We consider the dynamic pricing problem of a monopolist 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. We prove that optimal pricing policies induce a perception of monotonic prices, whereby consumers always perceive a discount, respectively surcharge, relative to their expectations. The effect is that of a skimming or penetration strategy. The firm’s optimal pricing path is monotonic on the long run, but not necessarily at the introductory stage. If consumers are loss averse, we show that optimal prices converge to a constant steady-state price, characterized by a simple implicit equation; otherwise, the optimal policy cycles. The range of steady states is wider the more loss averse consumers are. Steady-state prices decrease with the strength of the reference effect and with customers’ memory, all else equal. Offering lower prices to frequent customers may be suboptimal, however, if these 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. Our results hold under very general reference dependent demand models.