ORBIT learns the (β-1)-smooth oracle price map via local polynomial approximation and bandit convex optimization in a semiparametric contextual pricing model, achieving regret Õ(T^{(2β-1)/(4β-3)} + √(dT)) with a matching lower bound for fixed d.
Revenue Maximization Under Sequential Price Competition Via The Estimation Of s-Concave Demand Functions
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abstract
We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices (which are made public) and subsequently observe their respective demand (not made public). The demand function of each seller depends on all sellers' prices through a private, unknown, and nonlinear relationship. We propose a dynamic pricing policy that uses semi-parametric least-squares estimation and show that when the 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.
years
2026 2verdicts
UNVERDICTED 2representative citing papers
The paper establishes equilibrium existence and uniqueness for nonlinear utility consumer networks under contraction conditions and proposes a shape-constrained isotonic regression approach with strict no-regret convergence for learning utilities in targeted monopoly pricing.
citing papers explorer
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Harnessing Unimodality in Semiparametric Contextual Pricing via Oracle Price Map Learning
ORBIT learns the (β-1)-smooth oracle price map via local polynomial approximation and bandit convex optimization in a semiparametric contextual pricing model, achieving regret Õ(T^{(2β-1)/(4β-3)} + √(dT)) with a matching lower bound for fixed d.
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Equilibrium and Pricing in Consumer Networks with Nonlinear Utilities: An Online Shape-Constrained Learning Approach
The paper establishes equilibrium existence and uniqueness for nonlinear utility consumer networks under contraction conditions and proposes a shape-constrained isotonic regression approach with strict no-regret convergence for learning utilities in targeted monopoly pricing.