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

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.