From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms

TL;DR

This paper develops a novel demand learning algorithm for third-party platform pricing, addressing confounding issues and supply noise, with theoretical guarantees and real-world validation.

Contribution

It introduces an optimal regret algorithm for demand learning under confounding, utilizing instrumental variables and neural networks, with practical applications demonstrated.

Findings

Optimal regret of  ilde{ ext{O}}(\sqrt{T} ext{ or } \sigma_S^{-2})

Supply-side noise causes a phase transition in demand learnability

First efficiency guarantee for neural network-based demand estimation

Abstract

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only the equilibrium price and quantity are observable, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of $\Tilde{\cO}(\sqrt{T}\wedge\sigma_S^{-2})$. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we demonstrate the practical applicability of our approach through simulations and real-world data from Zomato and Lyft.