Papers › Revenue Maximization Under Sequential Price Competition Via The Estimation Of...
Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions
Daniele Bracale, Moulinath Banerjee, Cong Shi, Yuekai Sun
We consider price competition among multiple sellers over a selling horizon of T periods. In each period, sellers simultaneously offer their prices and subsequently observe their respective demand that is unobservable to competitors. The demand function for each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. To address this challenge, we propose a semi-parametric least-squares estimation of the nonlinear mean function, which does not require sellers to communicate demand information. We show that when all sellers employ our policy, their prices converge at a rate of O(T^(-1/7)) to the Nash equilibrium prices that sellers would reach if they were fully informed. Each seller incurs a regret of O(T^(5/7)) relative to a dynamic benchmark policy. A theoretical contribution of our work is proving the existence of equilibrium under shape-constrained demand functions via the concept of s-concavity and establishing regret bounds of our proposed policy. Technically, we also establish new concentration results for the least squares estimator under shape constraints. Our findings offer significant insights into dynamic competition-aware pricing and contribute to the broader study of non-parametric learning in strategic decision-making.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections