“Randomized Pricing of a Storable Good in the Presence of Consumer Stockpiling”
by Selçuk Karabatı
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Randomized pricing is a frequently observed practice in online retailing. Strategic customers adjust their purchase quantities and/or time their purchases by taking into account their beliefs about the timing of deals. We study a randomized pricing problem of an online retailer selling a single storable product to two customer segments that are heterogeneous in their product valuations and holding costs. To maximize their utility, these customers can stockpile a product without increasing their consumption. The retailer’s objective is to maximize expected revenue using a randomized pricing strategy that serves as an intertemporal price discrimination mechanism. We study two cases where customers act strategically using endogenously or exogenously set stockpile-up-to levels in response to randomized pricing. We first develop a model for the expected revenue maximization problem when stockpile-up-to levels are endogenous, and present a decomposition scheme to effectively find the optimal randomized policy. For the case of exogenously set stockpile-up-to levels, we characterize the retailer’s optimal price randomization strategy with a first-order equation. With a computational study, we shed light on the segments’ attributes that make price randomization an attractive strategy for the retailer. Our analysis indicates that, from the retailer’s viewpoint, price randomization can be an effective alternative to commitment to a single and time- independent price in the presence of segments having similar sizes and marked differences in product valuations. We finally demonstrate that the results are also valid for the case of patient customers that wait to make one-time purchases in anticipation of a lower future price.