Dynamic Pricing with Demand Learning and Reference Effects

We consider a seller's dynamic pricing problem with demand learning and reference effects. We first study the case in which customers are loss-averse: they have a reference price that can vary over time, and the demand reduction when the selling price exceeds the reference price dominates the demand increase when the selling price falls behind the reference price by the same amount. Thus, the expected demand as a function of price has a time-varying kink and is not differentiable everywhere. The seller neither knows the underlying demand function nor observes the time-varying reference prices. In this setting, we design and analyze a policy that (i) changes the selling price very slowly to control the evolution of the reference price and (ii) gradually accumulates sales data to balance the trade-off between learning and earning. We prove that, under a variety of reference-price updating mechanisms, our policy is asymptotically optimal; that is, its T-period revenue loss relative to a clairvoyant who knows the demand function and the reference-price updating mechanism grows at the smallest possible rate in T. We also extend our analysis to the case of a fixed reference price and show how reference effects increase the complexity of dynamic pricing with demand learning in this case. Moreover, we study the case in which customers are gain-seeking and design asymptotically optimal policies for this case. Finally, we design and analyze an asymptotically optimal statistical test for detecting whether customers are loss-averse or gain-seeking.

Automated summary

This study considers a seller's dynamic pricing problem with demand learning and reference effects. The research focuses on loss-averse customers who have a reference price that can vary over time. The study designs and analyzes a policy for the seller to slowly change the selling price and accumulate sales data to control the evolution of the reference price and balance the trade-off between learning and earning. The study proves the asymptotic optimality of the policy under various reference-price updating mechanisms and extends the analysis to fixed reference price cases.