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.

Loss Functions for Discrete Contextual Pricing with Observational Data

“…There has been significant recent interest in learning contextual pricing algorithms, which incorporate customer and product features to make pricing decisions. A common approach is the "predict then optimize" framework, where a demand function is estimated then optimized to find the optimal pricing policy (Chen et al 2015, Ferreira et al 2016, Dubé and Misra 2017, Baardman et al 2018, Alley et al 2019, Biggs et al 2021. For contextual policy learning, there are approaches which assume access to the valuation distribution or data (Mohri andMedina 2014, Elmachtoub et al 2021).…”

“…Products features can also be differentiated, for example in airline ticket pricing, prices are differentiated based on time of day, day of week, and how far in advance the tickets are purchased (Shaw 2016). Many companies have shown an interest in contextual pricing including Airbnb (Ye et al 2018), Stubhub (Alley et al 2019) and Ziprecruiter (Dubé and Misra 2017), where in addition to increased revenue, the benefits include automation of pricing that needs to be done over a large scale.…”

“…A common approach used for contextual pricing is to estimate a demand function from the data, and use it to find the optimal price for each customer (Chen et al 2015, Ferreira et al 2016, Dubé and Misra 2017, Baardman et al 2018, Alley et al 2019, Biggs et al 2021. In particular, the demand function estimates the probability of each customer purchasing a product as a function of the price they are offered and their features.…”

Stochastic Cutting Planes for Data-Driven Optimization

“…-Treatment Effect Estimation: This includes a wide range of data-driven optimization problems in pricing and policy treatment effect estimation (see e.g. Rivers and Vuong 1988, Blundell and Powell 2004, Alley et al 2019 where the loss is constructed from a parametric or semi-parametric loss function and there are further constraints on the parameters (nonnegativity, bounds, etc). Many of these problems might involve non-convex loss functions, but they are usually solved by methods that assume convexity (e.g.…”

Convex Loss Functions for Contextual Pricing with Observational Posted-Price Data

“…A popular approach in practice is a predict then optimize, or direct method approach, whereby an intermediate contextual demand function is estimated to predict the probability a customer purchases at a given price, and then optimized to maximize revenue (Chen et al 2015, Ferreira et al 2016, Dubé and Misra 2017, Alley et al 2019, Baardman et al 2020, Biggs et al 2021b.…”