Dynamic Pricing Under a General Parametric Choice Model

  • Authors:

  • Josef Broder;Paat Rusmevichientong

  • Affiliations:

  • Center for Applied Mathematics, Cornell University, Ithaca, New York 14850;Marshall School of Business, University of Southern California, Los Angeles, California 90089

  • Venue:
  • Operations Research
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

We consider a stylized dynamic pricing model in which a monopolist prices a product to a sequence of T customers who independently make purchasing decisions based on the price offered according to a general parametric choice model. The parameters of the model are unknown to the seller, whose objective is to determine a pricing policy that minimizes the regret, which is the expected difference between the seller's revenue and the revenue of a clairvoyant seller who knows the values of the parameters in advance and always offers the revenue-maximizing price. We show that the regret of the optimal pricing policy in this model is $\Theta(\sqrt T)$, by establishing an $\Omega(\sqrt T)$ lower bound on the worst-case regret under an arbitrary policy, and presenting a pricing policy based on maximum-likelihood estimation whose regret is $\cal{O}(\sqrt T)$ across all problem instances. Furthermore, we show that when the demand curves satisfy a “well-separated” condition, the T-period regret of the optimal policy is Θ(log T). Numerical experiments show that our policies perform well.