Price Optimization for a Multistage Choice Model
研究了在多阶段选择模型中，卖家如何根据顾客历史购买行为制定价格，以最大化利润，并发现最优定价满足修正的等调整加价性质，且前瞻性顾客会促使卖家调整各阶段价格。
Considering the real-world situations where a customer’s purchase choices in previous stages can influence the prices she encounters in subsequent stages, this research examines the multiproduct price optimization problem under a multistage choice model. Particularly, the seller commits to a multistage pricing policy and determines product prices based on the customer’s purchase history, and the customer makes purchase decisions such that the total expected utility is maximized. We show that the pricing problem has a unique optimal solution under some mild conditions and the optimal solution satisfies a modified equal adjusted markup property. Based on the property, the problem can be solved efficiently by reducing it to a single-dimensional search problem. Moreover, the optimal pricing policy has an important property, namely, the product with a higher adjusted markup in earlier stages should always lead to lower prices in subsequent stages. We also show that compared to customers who are myopic, the seller should offer higher first-stage prices and lower second-stage prices to forward-looking customers, which will lead to a higher profit. Numerical analyses are also conducted to demonstrate the above results.