Pricing Today, Shaping Tomorrow: Contextual Dynamic Pricing in Purchase-Driven Evolving Systems

arXiv:2611.00719v1 Announce Type: cross Abstract: Across diverse markets, it is important for firms to balance attracting customers with managing operational conditions, such as workloads and delivery times. Dynamic pricing plays a central role in this tradeoff, as the orders generated today can change the conditions faced by future customers. We develop a novel framework for contextual dynamic pricing with an observed shared state and unknown purchase-driven transitions. The valuation model allows unknown mean functions of customer covariates and state, unknown state-specific scales and a common unknown standardized noise distribution. We propose Shadow-Adjusted Pricing in Evolving Systems (SHAPE), which incorporates a purchase's future revenue consequences into current pricing. Purchase-shadow adjustment and scale standardization reveal a common one-dimensional oracle price map across states, allowing SHAPE to retain its pricing history across value updates without repeating coarse exploration. The same active sales records support price-map learning and joint updates of continuation values and purchase shadows, without fitting the noise distribution or full transition matrices. To support this reuse under purchase-driven feedback, we establish pricing guarantees for history-dependent inputs and stability bounds for the joint updates. Under regularity, coverage and design conditions, we obtain sublinear expected regret against a finite-horizon dynamic oracle for linear, H\"older and sparse linear mean models. For affine valuations at fixed state and feature dimensions, SHAPE matches the static semiparametric minimax time exponent up to logarithmic factors for every fixed noise-tail smoothness order $\beta\ge2$. Numerical experiments further demonstrate the appealing performance of SHAPE.