Technical Note—Dynamic Pricing with Gain-Seeking Reference Price Effects

Abstract

We study a dynamic pricing problem of a firm facing reference price effects at an aggregate demand level, where demand is more sensitive to gains than losses. We find that even the myopic pricing strategy belongs to one type of discontinuous maps, which can exhibit complex dynamics over time. Our numerical examples show that, in general, the optimal pricing strategies may not admit any simple characterizations and the resulting reference price/price dynamics can be very complicated. We then show for a special case that a cyclic skimming pricing strategy is optimal, and we provide conditions to guarantee the optimality of high-low pricing strategies.

Efficient Algorithms for the Dynamic Pricing Problem with Reference Price Effect

“…Interestingly, this case is similar to the special case, the so-called 2-(K = 1, Q = ∞) case in Ahn et al (2007), even though we have a totally different model. Also, Assumption 5 is found in the empirical studies by Hu et al (2015) to be a good approximation to the demands faced in practice.…”

“…Nasiry and Popescu (2011) consider the dynamic pricing problem with a peak-end based reference price model and loss-averse consumers; they also conclude the observation by . Hu et al (2015), on the other hand, show that when consumers are gain-seeking, even myopic pricing strategy can lead to complicated dynamics and they prove for a special case that a cyclic skimming pricing strategy is optimal. It is worth mentioning that all of the above papers assume stationary demand.…”

Intertemporal Price Discrimination with Time-Varying Valuations

“…The very recent work of Caldentey et al (2016) considers an intertemporal pricing problem under minimax regret where both strategic and myopic patient-customers are considered. Finally, two recent notes (Wang (2016) and Hu et al (2016)) tackle the problem of intertemporal pricing in the presence of reference price effects in an infinite horizon setting with discounted revenue.…”

Implications for Firms with Limited Information to Take Advantage of Reference Price Effect in Competitive Settings

“…This helps us to understand the fact that firms encourage consumers to recall reference price. Hu et al [22] considered a gain-seeking reference price effect model and identified conditions on parameters such that a highlow pricing strategy is optimal. Besides these studies, some valuable insights are also reached by integrating pricing with other decision variables, such as advertising strategy [8,23], replenishment policies [24,25], and preservation technology investment [26].…”

“…Although these two assumptions seem restrictive, they can provide good approximation to some practical scenarios [22]. We use ( ) = 4 + 1 3 + 2 2 + 3 + 4 to denote the characteristic polynomial of four-dimensional systems.…”