Robust multiperiod dynamic pricing under ambiguity

Dynamic pricing poses a significant challenge for firms operating in markets with limited data and high demand uncertainty. This study introduces a robust multiperiod pricing approach that minimises worst-case regret in scenarios where only the range of customer valuations is known. By employing the minimax regret criterion, the approach derives optimal pricing strategies for both single- and multicustomer settings without relying on probabilistic demand assumptions. For single-customer scenarios, a backward induction algorithm yields a logarithmic upper bound on cumulative regret. For multiple customers, a forward-looking algorithm dynamically adjusts prices on the basis of observed sales, significantly outperforming parametric and nonparametric benchmarks. We also evaluate the pricing policies in numerical experiments using an average-profit-based performance measure. Across diverse valuation distributions, the proposed methodology achieves more than 95% of the optimal profit on average, with peak performance exceeding 99% in some cases. These findings address a critical gap in dynamic pricing under ambiguity, offering firms actionable tools for navigating uncertain and data-scarce environments with confidence and adaptability.