Cyclic Pricing with Strategic Waiting Customers and Population Dynamics
Author | : Zheyi Li |
Publisher | : |
Total Pages | : 0 |
Release | : 2022 |
Genre | : |
ISBN | : |
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We consider continuous-time dynamic pricing in the presence of strategic waiting customers and their population dynamics. The firm makes the pricing decision with a finite menu of prices each time. Customers arrive at a constant rate with heterogeneous valuations. Customers purchase if the current price is less than their corresponding valuations. The remaining customers are strategic: they may leave or wait for future clearance sales, and the leaving rate can be population-contingent. The firm has the option to offer a clearance price to attract all waiting customers to purchase. We build a continuous-time model by exploiting impulse control. For a two-price menu, the optimal pricing policy is a cyclic pricing strategy that starts with a regular price and ends at a clearance price. For a multi-price menu, in contrast to the existing literature, we show that the optimal dynamic pricing policy can be either a textit{pump and dump cyclic} or textit{generalized pump and dump cyclic} strategy. Which strategy is optimal is determined by the sign of the effective marginal leaving rate. We provide analytical solutions for the cycle length and the optimal pricing path. Our results provide new explanations for the popularity of periodic clearance sales with penetration pricing and skimming pricing in practice. Our findings also provide guidelines on carrying out dynamic pricing with the customer leaving behaviors. Numerically, we show that ignoring cyclic pricing in the presence of strategic waiting customers can lead to a significant profit loss.