Dynamic Pricing and Learning with Finite Inventories

We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy that maximizes the expected revenue. Inference on the unknown parameters is made by maximum likelihood estimation. We show that this problem satisfies an endogenous-learning property, which means that the unknown parameters are learned on-the-fly if the chosen selling prices are sufficiently close to the optimal ones. We show that a small modification to the certainty equivalent pricing strategy - which always chooses the optimal price w.r.t. current parameter estimates - satisfies Regret(T) = O(log2(T)), where Regret(T) measures the expected cumulative revenue loss w.r.t. a clairvoyant who knows the demand distribution. We complement this upper bound by showing an instance for which the regret of any pricing policy satisfies Ω(logT)

Dynamic Pricing and Learning with Finite Inventories

We study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution. Products are sold during selling seasons of finite length, and inventory that is unsold at the end of a selling season perishes. The goal of the seller is to determine a pricing strategy that maximizes the expected revenue. Inference on the unknown parameters is made by maximum likelihood estimation. We show that this problem satisfies an endogenous-learning property, which means that the unknown parameters are learned on-the-fly if the chosen selling prices are sufficiently close to the optimal ones. We show that a small modification to the certainty equivalent pricing strategy - which always chooses the optimal price w.r.t. current parameter estimates - satisfies Regret(T) = O(log2(T)), where Regret(T) measures the expected cumulative revenue loss w.r.t. a clairvoyant who knows the demand distribution. We complement this upper bound by showing an instance for which the regret of any pricing policy satisfies Ω(logT)

Including Limited Partners in the Diversity Jurisdiction Analysis

This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29–30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition