ecommerce pricing teams

Abstract: Repeated Bertrand competition is a stringent benchmark for algorithmic pricing: in homogeneous-goods markets, standard learning procedures typically select the stage-game Nash outcome with prices near marginal cost. We show that LLM pricing agents can escape this benchmark, depending on deployment decisions. LLMs outperform standard online learners through faster adaptation, but this advantage largely disappears against full-information learners. An extracted surrogate algorithm illustrates how LLMs in specific deployments profit from regularly undercutting slower learners. Agents that post one price every period from raw market histories that include rival prices can sustain supracompetitive regimes in self-play. Agents that periodically emit probability distributions from summarized histories of their own profits instead move toward the competitive region in self-play. Markets mixing these interfaces can generate dynamic regimes in which LLMs establish a high-price anchor and regularly undercut it to capture demand. These regimes can keep both competitors' prices above marginal cost. Deployment choices shape these outcomes, shifting the focus from stationary equilibria to dynamic pricing regimes.

Abstract: We study online dynamic pricing with censored demand, where an arbitrary inventory level is revealed before pricing and may adapt to past observations, while demand follows an unknown, price-dependent distribution that is stationary over time. For a horizon of $T$ rounds, Xu et al. [2026] achieved $\widetilde{\mathcal{O}}(\sqrt{T})$ regret under restrictive structural assumptions including linear demand, price-independent additive noise, and conditions relating inventory levels to the noise support. Our first contribution is to extend this framework to a substantially more general and statistically harder nonparametric setting, requiring only the natural assumption that expected sales are nonincreasing in price and allowing nonlinear demand curves and price-dependent noise. For this model, we first propose a simple baseline, Double-Grid-UCB, which discretizes both price and inventory and achieves $\widetilde{\mathcal{O}}(T^{3/4})$ expected regret using separate revenue estimates for each price-inventory grid pair. Then, we develop Threshold-UCB, which improves the expected regret to $\widetilde{\mathcal{O}}(T^{2/3})$. Unlike Double-Grid-UCB, Threshold-UCB reuses sales observations across inventory levels through shared estimates of demand-tail probabilities, allowing the same data to support revenue upper bounds for multiple inventories rather than a single inventory bin. We also complement this upper bound with an $Ω(T^{2/3})$ lower bound via a reduction from stochastic posted pricing, establishing its minimax optimality. Finally, extensive experiments across inventory processes, demand functions, and noise models demonstrate consistently superior performance of Threshold-UCB over benchmark algorithms.