Dynamic pricing in the presence of reference price effect and consumer strategic behaviour

Abstract

This paper presents a model for designing two-stage dynamic pricing strategies when the seller faces strategic consumers in the presence of a reference price effect. The consumers form the utilities of two sequential periods based on anticipated future retail price in the second period and current retail price in the first period as the reference price, and then choose the purchasing timing, representing strategic behaviour. We first consider a centralised system where the seller chooses between two pricing policies: markdown pricing and markup pricing under a centralised system, and find that the seller will not adopt a markup pricing policy. We derive equilibrium prices and optimal pricing strategies for the seller under markdown pricing policy using equilibrium theory and backward induction method. We find that the seller’s profit decreases with the consumer strategic behaviour, and increases (decreases) with the reference price effect when consumer strategic behaviour is low (high), indicating a non-monotonity with respect to the coexistence of consumer strategic behaviour and reference price effect. We then extend our study from a centralised system to a decentralised system and find that double marginalisation is effectively weakened by the two effects. Interestingly, the centralised structure may not always be optimal relative to a decentralised structure, indicating a non-monotone relationship between the wholesale price and the profit in decentralised structure.

Keywords:

• supply chain management
• two-stage dynamic pricing
• consumer strategic behaviour
• reference price effect

Acknowledgements

All authors contribute equally to the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Layth C. Alwan http://orcid.org/0000-0002-5653-3098

Notes

1 In the US, there are comparable one-day price slashing days, most notably, Black Friday and Cyber-Monday.

2 Due to strategically waiting for purchase in pursuit of price reduction, it may substantively hurt the firm’s profit (Coase 1972). To avoid this adverse effect, the firm may have the incentive to reduce or eliminate the price difference between periods by choosing pricing strategy such as Every Day Low Pricing (EDLP).

3 The Conjecture discovers that infinitely patient consumers may impose the monopolist to charge a price not exceeding marginal cost.

4 Under case I (PP strategy), all consumers make purchase in period 2. The CSB has no impact on the profit. The RPE has positive effect on the profit, which is identical to the benchmark case.

5 In this study, we assume that the seller has no discount for the profit. If the profit discount is considered, Lemma 4 may not always hold when the discount is relatively low because the seller puts greater emphasis on the profit in period 1. For example, if the profit discount is lower than a certain threshold, the seller will adopt a markup strategy by encouraging the consumers to make purchases in the first period, so that no purchase happens in the second period. As a consequence, the CSB and RPE have no effects on the consumer’s purchasing decision. Since this study investigates the interaction of the CSB and RPE, we assume that there is no profit discount or that the discount is at a low level such that the seller adopts the markdown price strategy. Note that the profit discount may affect the seller’s decisions by interacting with the two effects, and an intuitive consequence is the decrease of his price and profit. However, the qualitative results in this study still hold. To simplify the mathematical results and for analytical convenience, we assume that the seller has no profit discount.

6 When the consumers observe the retail price $p_1$ in period 1, they rationally anticipate the retail price $p_2$ the retailer will set. Such rationality can be realised in a fluid internet-based environment with information and communication technology. For example, the large number of e-commerce platforms, such as Amazon.com and Taobao.com, enable customers to easily search for a variety of product information, such as historical sales prices, the prices of homogeneous products of other brands, and online evaluations, all of which provide a basis for rationally strategic purchasing decisions. After anticipating the future price, the consumers make purchase to maximise the expected utilities. If the expected utility in period 1 is higher than that in period 1, and is non-negative, the consumer makes early purchase in this period. Otherwise, the consumer makes late purchase in period 2 if the utility is non-negative.

7 Due to similar properties of wholesale prices to retail prices, we omit the analysis here.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 71671173], [grant number 71371008], [grant number 71731010] and [grant number 71520107002].