59 Pages Posted: 20 Dec 2017 Last revised: 24 Oct 2020
Date Written: October 26, 2019
We study a monopoly's robust pricing problem in which the seller does not know the customers' valuation distribution but knows its mean and variance. Such minimum requirement of information only requires that the pricing managers be able to answer two questions: How much will your targeted customers pay on average? And, to measure your confidence in the previous answer, what is the standard deviation of customer valuations? We focus on the maximin profit criterion and derive distribution-free upper and lower bounds on the profit function. By maximizing the profit lower bound, we obtain the optimal robust price in closed form as well as its distribution-free, worst-case performance bound. The optimal robust price is lower than the mean valuation and than the optimal prices under the minimax absolute regret and maximin relative performance criterion. The more variable the valuation distribution, the lower the optimal robust price should be. Moreover, we observe that having certain additional information about the distribution may not be of significant additional value. We then extend the single-product result to study the robust pure bundle pricing problem where the seller only knows the mean and variance of each product, and provide easily verifiable, distribution-free, sufficient conditions that guarantee the pure bundle to be more robustly profitable than a la carte (i.e., separate) sales. Finally, we provide a distribution-free, worst-case performance guarantee for pricing under a bundling heuristic scheme in which customers choose from buying either a single product or a pure bundle. The robust price is in closed form and hence is easily computed. Its interpretation can be easily explained to pricing managers and there exists a natural connection with the newsvendor ordering decision that is widely taught in the MBA classrooms.
Keywords: pricing, robust optimization
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