From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms
This work addresses pricing optimization for platforms like Zomato and Lyft, offering a novel method for demand learning with practical applications.
The paper tackles the problem of dynamic service fee pricing on third-party platforms under confounding from strategic agents, achieving an optimal regret bound of \Tilde{\O}(√T ∧ σ_S^{-2}) and revealing a phase transition in regret due to supply-side noise.
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 $\Tilde{\cO}(\sqrt{T}\wedgeσ_S^{-2})$. 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.