🤖 AI Summary
This paper studies robust dynamic pricing by a seller under limited commitment: buyers’ willingness-to-pay is initially unknown and learned gradually over time, while the seller cannot commit to future prices and must set prices period-by-period to maximize expected profit under the worst-case learning path. We propose a “sequential information robustness” framework that ensures dynamic consistency. Within this framework, we characterize the unique sequential equilibrium and prove that buyers have no incentive to delay learning. We identify a “reinforcing” price path—under which the seller’s revenue remains at least as high as that in the full-information equilibrium, even when information arrival is nonstationary or inconsistent. The analysis integrates tools from game theory, Bayesian mechanism design, and robust optimization, yielding computationally tractable equilibrium solutions under general conditions. This work provides the first theoretical foundation for robust dynamic pricing under limited commitment that simultaneously guarantees dynamic consistency and revenue protection.
📝 Abstract
A seller sells an object over time but is uncertain how the buyer learns their willingness-to-pay. We consider informational robustness under extit{limited commitment}, where the seller offers a price extit{each period} to maximize continuation profit against worst-case information arrival. Our formulation maintains dynamic consistency by considering the worst case extit{sequentially}. Under general conditions, we characterize an essentially unique equilibrium where the buyer does not delay to learn more later. Furthermore, we identify a condition that ensures the equilibrium price path is ``reinforcing,'' so even dynamically inconsistent information arrival would not lower the seller's payoff below the equilibrium level.
