Erschienen in:Marshall School of Business Working Paper ; No. 17-6
Umfang:
1 Online-Ressource (47 p)
Sprache:
Englisch
DOI:
10.2139/ssrn.2855843
Identifikator:
Entstehung:
Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments December 31, 2017 erstellt
Beschreibung:
We study the pricing problem faced by a firm that sells a large number of products, described via a wide range of features, to customers that arrive over time. Customers independently make purchasing decisions according to a general choice model that includes products features and customers' characteristics, encoded as d-dimensional numerical vectors, as well as the price offered.The parameters of the choice model are a-priori unknown to the firm, but can be learned as the (binary-valued) sales data accrues over time. The firm's objective is to minimize the regret, i.e., the expected revenue loss against a clairvoyant policy that knows the parameters of the choice model in advance, and always offers the revenue-maximizing price. This setting is motivated in part by the prevalence of online marketplaces that allow for real-time pricing.We assume a structured choice model, parameters of which depend on s out of the d product features. We propose a dynamic policy, called Regularized Maximum Likelihood Pricing (RMLP) that leverages the (sparsity) structure of the high-dimensional model and obtains a logarithmic regret in T. More specifically, the regret of our algorithm is of O(s log d log T). Furthermore, we show that no policy can obtain regret better than O(s (log d log T))