On dynamic pricing under model uncertainty

Abstract

We formulate and solve a robust dynamic pricing problem for an ambiguity‐averse agent who faces an uncertain probabilistic law governing the realized demand for a single product. Specifically, the pricing problem is framed as a stochastic game that involves a maximizing player (the “agent”) and a minimizing player (“nature”) who promotes robustness by distorting the agent's beliefs within prescribed limits. Our methodology builds on the commonly used entropic approach in the literature but can be utilized to generate a much more versatile class of uncertainty sets. We derive the optimal pricing strategy and the corresponding value function by applying stochastic dynamic programming and solving a version of the Bellman–Isaacs equation. The usefulness of our framework is illustrated by two special cases. Finally, a carefully designed numerical example exposes the value of model robustness.