Pricing for Heterogeneous Products: Analytics for Ticket Reselling

Abstract

Problem definition: We present a data-driven study of the secondary ticket market. In particular, we are primarily concerned with accurately estimating price sensitivity for listed tickets. In this setting, there are many issues including endogeneity, heterogeneity in price sensitivity for different tickets, binary outcomes, and nonlinear interactions between ticket features. Our secondary goal is to highlight how this estimation can be integrated into a prescriptive trading strategy for buying and selling tickets in an active marketplace. Academic/practical relevance: We present a novel method for demand estimation with heterogeneous treatment effect in the presence of confounding. In practice, we embed this method within an optimization framework for ticket reselling, providing the ticket reselling platform with a new framework for pricing tickets on its platform. Methodology: We introduce a general double/orthogonalized machine learning method for classification problems. This method allows us to isolate the causal effects of price on the outcome by removing the conditional effects of the ticket and market features. Furthermore, we introduce a novel loss function that can be easily incorporated into powerful, off-the-shelf machine learning algorithms, including gradient boosted trees. We show how, in the presence of hidden confounding variables, instrumental variables can be incorporated. Results: Using a wide range of synthetic data sets, we show this approach beats state-of-the-art machine learning and causal inference approaches for estimating treatment effects in the classification setting. Furthermore, using National Basketball Association ticket listings from the 2014–2015 season, we show that probit models with instrumental variables, previously used for price estimation of tickets in the resale market, are significantly less accurate and potentially misspecified relative to our proposed approach. Through pricing simulations, we show our proposed method can achieve an 11% return on investment by buying and selling tickets, whereas existing techniques are not profitable. Managerial implications: The knowledge of how to price tickets on its platform offers a range of potential opportunities for our collaborator, both in terms of understanding sellers on their platform and in developing new products to offer them.