The Value of Information in Resource-Constrained Pricing

TL;DR

This paper analyzes how demand prediction errors impact dynamic pricing under capacity constraints, identifying thresholds for effective forecasts and methods to reduce uncertainty, with theoretical and experimental validation.

Contribution

It introduces a threshold for demand forecast accuracy that ensures near-optimal pricing, and proposes surrogate models to reduce variance in demand estimation.

Findings

Forecast accuracy threshold for logarithmic regret regime

Surrogate models reduce demand estimation variance by up to (1-ρ^2)

Algorithms stabilize prices near capacity boundaries without non-degeneracy assumptions

Abstract

Firms that price perishable resources -- airline seats, hotel rooms, seasonal inventory -- now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate prediction can irreversibly deplete inventory needed for future periods. We study how prediction uncertainty propagates into dynamic pricing decisions with linear demand, stochastic noise, and finite capacity. A certified demand forecast with known error bound~$\epsilon^0$ specifies where the system should operate: it shifts regret from $O(\sqrt{T})$ to $O(\log T)$ when $\epsilon^0 \lesssim T^{-1/4}$, and we prove this threshold is tight. A misspecified surrogate model -- biased but correlated with true demand -- cannot set prices directly but reduces learning variance by a factor of $(1-\rho^2)$ through control variates. The two mechanisms compose: the forecast determines the regret regime; the surrogate tightens estimation within it. All algorithms rest on a boundary attraction mechanism that stabilizes pricing near degenerate capacity boundaries without requiring non-degeneracy assumptions. Experiments confirm the phase transition threshold, the variance reduction from surrogates, and robustness across problem instances.