Simultaneously Learning and Optimizing Using Controlled Variance Pricing

Arnoud V. den Boer () and Bert Zwart ()
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Arnoud V. den Boer: Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands; and University of Amsterdam, 1098 XH Amsterdam, The Netherlands
Bert Zwart: Centrum Wiskunde and Informatica, 1098 XG Amsterdam, The Netherlands; and Department of Mathematics, VU University Amsterdam, 1081 HV Amsterdam, The Netherlands

Management Science, 2014, vol. 60, issue 3, 770-783

Abstract: 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. This paper was accepted by Assaf Zeevi, stochastic models and simulation.

Keywords: dynamic pricing; sequential decision problems; statistical learning (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (45)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:60:y:2014:i:3:p:770-783

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