Informational Robustness in Intertemporal Pricing

Abstract

We introduce a robust approach to study dynamic monopoly pricing of a durable good in the face of buyer learning. A buyer receives information about her willingness-to-pay for the seller’s product over time, and decides when to make a one-time purchase. The seller does not know how the buyer learns, but commits to a pricing strategy to maximize profits against the worst-case information arrival process. We show that a constant price path delivers the robustly optimal profit, with profit and price both lower than under known values. Thus, under the robust objective, intertemporal incentives do not arise at the optimum, despite the possibility for information arrival to influence the timing of purchases. We delineate whether constant prices remain optimal (or not) when the seller seeks robustness against a subset of information arrival processes. As part of the analysis, we develop new techniques to study dynamic Bayesian persuasion.

Robust Mechanisms Under Common Valuation

“…I show that when N = 1, the revenue guarantee of the exponential price auction is exactly the seller's optimal revenue at the Roesler-Szentes information structure, thus proving the optimality of the revenue guarantee. 3 The Roesler-Szentes information structure and the exponential price auction have proved to be useful in the study of a robust dynamic pricing problem by Libgober and Mu (2017).…”

Robust Private Supply of a Public Good

“…More broadly, this paper is related to a strand of papers that focus on the case where the agents may have arbitrary high-order beliefs about each other unknown to the mechanism designer, e.g., Bergemann and Morris (2005), Chung and Ely (2007), Chen and Li (2018), Yamashita and Zhu (2018), Bergemann et al (2016Bergemann et al ( , 2017Bergemann et al ( , 2019, Du (2018), Brooks and Du (2021), Libgober and Mu (2021).…”

Learning Underspecified Models

“…Our paper differs from three main approaches to investigating the decision problem with underspecified models. The most prominent approach is that a decision-maker chooses his actions assuming uncertainty about the environment resolves in favor of the worst-case (e.g., Hansen and Sargent (2007), Carroll (2015), Carroll (2017), Du (2018) and Libgober and Mu (2021)). The choice that maximizes the objective under the worst conjecture will typically differ from the optimal solution against the truth, sometimes significantly so.…”