Dynamic Online Pricing with Incomplete Information Using Multiarmed Bandit Experiments

Abstract

Consider the pricing decision for a manager at a large online retailer, that sells millions of products.A manager must decide on real-time prices for each of these products. It is infeasible to have complete knowledge of demand curve for each product. A manager can run price experiments to learn about demand and maximize long run profits. There are two aspects that make this setting different from traditional brick-and-mortar settings. First, due to the number of products the manager must be able to automate pricing. Second, an online retailer can make frequent price changes. In this paper, we propose a dynamic price experimentation policy where the firm has incomplete demand information.For this general setting, we derive a pricing algorithm that balances earning profit immediately and learning for future profits. The proposed approach combines multi-armed bandit (MAB) algorithms statistical machine learning with partial identification of consumer demand from economic theory. Our automated policy solves this problem using a scalable distribution-free algorithm. We show that our method converges to the optimal price faster than standard machine learning MAB solutions to the problem. In a series of Monte Carlo simulations, we show that the proposed approach perform favorably compared to methods in computer science and revenue management.

Theory development in servitization through the application of fsQCA and experiments

“…Feit and Berman, 2019) will have a negative impact on the company's profitability during the test period, so-called adaptive testing is recommended (cf. Misra et al, 2019). This will continuously optimize the allocation of test subjects to the test conditions in terms of effectiveness-for example, maximizing the profit or the number of conversions.…”

Reinforcement learning for content's customization: a first step of experimentation in Skyscanner

“…The UCB approach allows to reach advantages, e.g. in terms of pricing applications when there is a need to identify the selling price without knowing the consumer demand: Misra et al (2019) highlighted that modified UCB algorithms statistical machine learning blended with partial identification of consumer demand, from economic theory, allowed to faster define the optimal price than other standard methods; Trov o et al (2015) with a modified UCB provide empirical evidence that proposed variations speed up the learning process in pricing applications. Generally, a modified UCB approach can significantly strike a balance between exploration and exploitation (Chen et al, 2020;Hussain and Michelusi, 2019;Xing et al, 2014).…”

Test & Roll: Profit-Maximizing A/B Tests

“…Chick and Inoue (2001) analyze a two-stage decision problem where the cost of the test is a fixed multiple of the sample sizes, rather than actual opportunity cost as we have here. In studying multi-armed bandits Schwartz et al (2017) and Misra et al (2019) use a test & roll as a benchmark, but they do not optimize the sample size. The closest work comes from the clinical trials literature, where Cheng et al (2003) defines the same test & roll problem with a finite "patient horizon" and approximates the optimal sample size for Bernoulli responses with beta priors.…”