Price discrimination with robust beliefs

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 per-formance 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 per-formance 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 ex-hibits 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.(c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Automated summary

This paper investigates second-degree price discrimination under unknown or imperfectly specified type distribution using ambiguity sets. A performance index is used as a measure of robustness, quantifying the worst-case attainment ratio between actual and ex-post optimal payoff. The paper provides a simple representation of this index and a solution to the robust identification problem, leading to a robust product portfolio with worst-case performance across consumer types. A numerical comparison evaluates the robust solution against alternative belief heuristics.