Simultaneously Learning and Optimizing Using Controlled Variance Pricing

• 成果类型: Article
• 署名作者: den Boer, Arnoud V.; Zwart, Bert
• 署名单位: Eindhoven University of Technology; University of Amsterdam; Vrije Universiteit Amsterdam
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2013.1788
• 发表日期: 2014
• 页码: 770-783
• 关键词: Dynamic pricing; sequential decision problems; Statistical learning

摘要

Price experimentation is an important tool for firms to find the optimal selling price of their products. It should be conducted properly, since experimenting with selling prices can be costly. A firm, therefore, needs to find a pricing policy that optimally balances between learning the optimal price and gaining revenue. In this paper, we propose such a pricing policy, called controlled variance pricing (CVP). The key idea of the policy is to enhance the certainty equivalent pricing policy with a taboo interval around the average of previously chosen prices. The width of the taboo interval shrinks at an appropriate rate as the amount of data gathered gets large; this guarantees sufficient price dispersion. For a large class of demand models, we show that this procedure is strongly consistent, which means that eventually the value of the optimal price will be learned, and derive upper bounds on the regret, which is the expected amount of money lost due to not using the optimal price. Numerical tests indicate that CVP performs well on different demand models and time scales.