Sequentially Optimal Pricing under Informational Robustness

TL;DR

This paper studies a seller's optimal pricing strategy over time when facing uncertain buyer learning, providing a worst-case, sequential equilibrium analysis that aligns with guaranteed profits under mild conditions.

Contribution

It introduces a sequentially robust pricing framework with limited commitment, characterizes a unique equilibrium, and shows profit equivalence with unrestricted learning scenarios under mild assumptions.

Findings

Characterization of a unique equilibrium under general conditions.

Equilibrium profit matches the guaranteed profit under mild prior assumptions.

Robust pricing strategy performs well against worst-case learning processes.

Abstract

A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under \textit{limited commitment}, where the seller offers a price \textit{each period} to maximize expected continuation profit against worst-case learning. Our formulation considers the worst case \textit{sequentially}. We characterize an essentially unique equilibrium under general conditions. We further show that, under mild conditions on the prior distribution, the equilibrium profit coincides exactly with the profit guaranteed by the equilibrium price path even under arbitrary (unrestricted) learning processes.