Online Dynamic Pricing of Complementary Products
Marco Mussi, Marcello Restelli
TL;DR
The paper tackles online pricing of complementary products by proposing CPP, a three-stage pipeline that aggregates substitutes, discovers leader–follower complementarities, and learns joint demand curves using heteroscedastic Gaussian processes. It introduces a practical, scalable framework that combines GP-based demand modeling with an integer-programming step to identify profitable complementarities, evaluated through simulations against independent-pricing baselines. Key contributions include a detailed online learning approach with GP-UCB for both independent and leader–follower structures, and an algorithmic mechanism to mine complementarity relations while managing computational constraints. Results show that exploiting inter-item dependencies yields revenue gains, particularly under strong cross-effects, while known-graph settings markedly improve learning speed and stability. The work provides a principled path toward coordinated multi-product pricing in data-rich environments, with clear directions for handling complexity and extending to richer consumer models.
Abstract
Traditional pricing paradigms, once dominated by static models and rule-based heuristics, are increasingly being replaced by dynamic, data-driven approaches powered by machine learning algorithms. Despite their growing sophistication, most dynamic pricing algorithms focus on optimizing the price of each product independently, disregarding potential interactions among items. By neglecting these interdependencies in consumer demand across related goods, sellers may fail to capture the full potential of coordinated pricing strategies. In this paper, we address this problem by exploring dynamic pricing mechanisms designed explicitly for complementary products, aiming to exploit their joint demand structure to maximize overall revenue. We present an online learning algorithm considering both positive and negative interactions between products' demands. The algorithm utilizes transaction data to identify advantageous complementary relationships through an integer programming problem between different items, and then optimizes pricing strategies using data-driven and computationally efficient multi-armed bandit solutions based on heteroscedastic Gaussian processes. We validate our solution in a simulated environment, and we demonstrate that our solution improves the revenue w.r.t. a comparable learning algorithm ignoring such interactions.