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.

Dynamic Pricing in Management Science

“…When the firm modifies the price for its good, consumers form a reference price that they adapt according to their perceptions on prices. Popescu and Wu (2007) show that in that case, when consumers perceive increases (resp. decreases) in prices, the optimal policy is penetration (resp.…”

“…Briesch et al (1997) suggest, according to certain empirical results, that the firm's past price is the best candidate as the reference price. Based on prospect theory, Popescu and Wu (2007) consider the problem of dynamic pricing of a monopoly when demand is sensitive to the firm's pricing history. In this framework, consumers have psychological biases in their purchasing decision.…”

A theory of price adjustment under loss aversion

“…Our dynamic approach confirms earlier findings that consumer loss aversion engenders price rigidity and allows us to study the asymmetry characteristics of pricing reactions to temporary and permanent demand shocks of different sign. Another study close to ours is Popescu and Wu (2007); although they analyze optimal pricing strategies in repeated market interactions with loss averse consumers and endogenous reference prices, they do not analyze the model's reaction to demand shocks.…”

Markdown or Everyday Low Price? The Role of Behavioral Motives

“…2 In contrast, a growing stream of literature relaxes these assumptions to investigate the impacts of consumers' behavioral issues on their purchase decisions and the seller's optimal pricing strategies. The behavioral issues that have been studied include loss aversion (Popescu and Wu 2007, Heidhues and Kőszegi 2008, Nasiry and Popescu 2011, Baron et al 2014), hyperbolic discounting (Su 2009, Baucells et al 2014, and anticipated regret (Diecidue et al 2012, Nasiry andPopescu 2012). We refer the reader toÖzer and Zheng (2012) for a comprehensive review of the behavioral pricing literature.…”