Price discrimination with robust beliefs

Jun Han and Thomas Weber

European Journal of Operational Research, 2023, vol. 306, issue 2, 795-809

Abstract: This paper considers the problem of second-degree price discrimination when the type distribution is unknown or imperfectly specified by means of an ambiguity set. As robustness measure we use a performance index, equivalent to relative regret, which quantifies the worst-case attainment ratio between actual payoff and ex-post optimal payoff. We provide a simple representation of this performance index, as the lower envelope of two boundary performance ratios, relative to beliefs that lie at the boundary of the ambiguity set. A characterization of the solution to the underlying robust identification problem is given, which leads to a robust product portfolio, for which we also determine the worst-case performance over all possible consumer types. For a standard linear-quadratic specification of the robust screening model, a worst-case performance index of 75% guarantees that the robust product portfolio exhibits a profitability that lies within a 25%-band of an ex-post optimal product portfolio, over all possible model parameters and beliefs. Finally, a numerical comparison benchmarks the robust solution against a number of alternative belief heuristics.

Keywords: Ambiguity; Pricing; Relative regret; Robust optimization; Screening (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:306:y:2023:i:2:p:795-809

DOI: 10.1016/j.ejor.2022.08.022

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