Dynamic Pricing under a Logit Choice Model

We consider a stylized dynamic pricing model in which a monopolist prices a product to a sequence of customers, who independently make purchasing decisions based on the price offered according to a logit choice model. The parameters of the logit 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. When there is a single unknown parameter, we show that the T -period regret is Θ(log T ), by establishing an Ω(log T ) lower bound on the regret under an arbitrary policy, and presenting a pricing policy based on maximum likelihood estimates that achieves a matching upper bound. For the case of two unknown parameters, we prove that the optimal regret is Θ( √ T ). Numerical experiments show that our policies perform well against several competing strategies.