Pricing for Heterogeneous Products: Analytics for Ticket Reselling

Abstract

We develop a framework for estimating price sensitivity in applications such as ticket reselling. This framework allows us to estimate heterogeneous price sensitivity that we subsequently embed in a price optimization model for ticket reselling. Due to the heterogeneous nature of tickets, the unique market conditions at the time each ticket is listed, and the sparsity of available tickets, demand estimation needs to be done at the individual ticket level. We introduce a double/orthogonalized machine learning method for a classification setting that allows us to isolate the causal effects of price on the outcome by removing the conditional effect of the ticket and market features. Furthermore, we introduce a novel loss function which can be easily incorporated into off the shelf machine learning algorithms, including gradient boosted trees and neural networks. We also show how in the presence of hidden confounding variables instrumental variables can be incorporated. Using a wide range of synthetic data sets, we show this approach beats state-of-the-art machine learning approaches for estimating price sensitivity in our setting, and prove analytical properties for this estimator. We then develop an optimization model for selling tickets on a secondary market, in which we incorporate the heterogeneous price sensitivity model. Leveraging data from a major ticket reseller, we show significant potential for impact in practice. More broadly, this paper develops a novel methodology for estimating heterogeneous treatment effects in classification settings that can be applied to other settings such as personalized pricing and estimating intervention effects in healthcare applications.