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Dynamic pricing strategies under repeated interactions

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The authors consider the dynamic pricing problem of a monopolist retailer in a market with repeated interactions, where customers are sensitive to the firm's pricing history, as summarized by a reference price. As the retailer manipulates prices, customers' reference prices adjust as an anchoring standard on the basis of actual price perceptions. Purchase decisions are made based on both actual and reference prices. The authors study a variety of demand models, including non-linear kinked S-shaped effects, as predicted by prospect theory, and relative difference models motivated by the Weber-Fechner law. They prove that optimal pricing policies induce a perception of monotonic prices, whereby consumers always perceive a discount relative to their expectations. The effect is that of a skimming or penetration strategy. In particular, they identify conditions for optimality of mono-tonic pricing strategies, and prove that optimal prices typically converge to a constant price that is characterized by a simple implicit equation. All else equal, this price decreases with the strength of the reference price effect, and with customers' memory. Offering lower prices to frequent customers may be suboptimal, however, if they are less sensitive to price changes than occasional buyers. The authors investigate extensions of these results for markets with heterogeneous consumers and multiple products. If managers ignore such long-term implications of their pricing strategy, the model indicates that they will systematically price too low and lose revenue.

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