Author: Denis Avetisyan
New research reveals how third-party platforms can dynamically adjust service fees to maximize learning and minimize regret in the face of uncertain demand.
This study develops a novel dynamic pricing algorithm leveraging instrumental variables and regret analysis to navigate supply noise and optimize fee structures.
Establishing effective pricing strategies is challenging when platforms lack complete demand information-a common scenario for third-party services. This paper, ‘From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms’, addresses this problem by developing a novel dynamic pricing algorithm that achieves optimal regret bounds despite the presence of confounding factors and supply-side noise. Our analysis reveals a fundamental trade-off between learnability and noise, alongside the surprising utility of non-i.i.d. actions as instrumental variables, and demonstrates the first efficiency guarantees for demand learning with deep neural networks. Can these techniques unlock more robust and responsive pricing models across diverse online marketplaces?
The Elusive Demand Curve: A Foundation for Rational Pricing
Accurate revenue optimization fundamentally relies on a clear understanding of demand curves – the graphical representation of how much of a product consumers will purchase at various prices. However, a significant challenge arises because market observations typically only reveal the equilibrium point – the specific price and quantity where supply and demand intersect. This limitation obscures the underlying demand curve itself, creating a situation where it’s difficult to discern how consumers would react to different price points. Consequently, businesses often operate with incomplete information, hindering their ability to set optimal prices and maximize profitability. Determining the true shape of the demand curve, therefore, becomes a critical, yet complex, undertaking for any revenue-focused strategy.
The difficulty in accurately mapping price to demand arises from persistent confounding issues – extraneous factors that obscure the true relationship. Observing only market equilibrium provides a single data point, a snapshot of price and quantity where supply and demand intersect, but fails to reveal how consumers would react to different prices. This creates ambiguity because unobserved variables, such as consumer preferences, complementary goods, or even external events, simultaneously influence both willingness to pay and the quantity purchased. Consequently, any observed correlation between price and quantity may not reflect a genuine causal link, leading to misinterpretations of the demand curve and potentially suboptimal pricing decisions. Isolating the independent effect of price requires sophisticated techniques to account for these hidden influences and disentangle the complex web of factors driving consumer behavior.
Conventional pricing strategies often falter when confronted with hidden variables influencing consumer behavior. These unobserved factors – ranging from subtle shifts in brand perception to external economic pressures not captured in standard datasets – introduce significant noise into demand estimation. Consequently, models relying solely on observed market data can misinterpret the true relationship between price and quantity demanded, leading to suboptimal pricing decisions. Businesses might inadvertently undervalue products with strong underlying demand or, conversely, overprice items where demand is artificially suppressed by these unquantified elements. This disconnect between modeled demand and actual consumer response underscores the need for more sophisticated techniques capable of accounting for these pervasive, yet often invisible, influences on purchasing decisions.
Algorithm1: A Dynamically Adaptive Pricing Mechanism
Algorithm1 is a dynamic service fee pricing method intended to improve demand estimation in situations where observed variables are correlated with unobserved factors that also influence demand. This algorithm operates by continuously adjusting service fees based on observed outcomes, aiming to discern genuine demand signals from spurious correlations. The method is designed to be applicable across diverse service platforms and is particularly useful when direct observation of demand is incomplete or biased. It differs from static pricing models by incorporating real-time feedback to refine pricing strategies, leading to improved revenue generation and resource allocation over time. The algorithm’s core functionality centers around iteratively updating fee levels and analyzing the resulting changes in service uptake to construct a more accurate model of underlying demand.
Algorithm1 utilizes instrumental variables (IV) to address the problem of endogeneity in demand estimation for dynamic pricing. Specifically, the algorithm identifies variables that correlate with service requests but do not directly influence the underlying willingness-to-pay, except through their impact on demand. These IVs are then used to construct an estimator for the causal effect of price on demand, effectively isolating the true demand signal from confounding factors such as seasonality or promotional activities. This approach allows the algorithm to more accurately determine the price elasticity of demand and optimize service fees, mitigating biases introduced by unobserved heterogeneity or simultaneous effects that would otherwise distort pricing decisions. The resulting demand estimate is then incorporated into a reinforcement learning framework for fee optimization.
Algorithm1 utilizes an exploration-then-commit strategy to optimize service fee pricing. Initially, the algorithm enters an exploration phase, systematically testing a range of fee levels to gather data on demand response. This phase prioritizes learning the relationship between fees and revenue, even at the potential cost of short-term gains. Following the exploration period, the algorithm transitions to a commit phase, where it exploits the learned information by consistently applying the fee level predicted to maximize cumulative revenue. The duration of the exploration phase is adaptively determined, balancing the need for continued learning against the benefits of exploiting known profitable fee levels. This approach aims to minimize cumulative regret over time T by efficiently allocating resources between gathering information and maximizing immediate profits.
Algorithm1 is designed to maximize cumulative revenue by minimizing optimal regret, a metric representing the difference between the revenue earned and the revenue that would have been earned by consistently choosing the optimal fee. The algorithm achieves a performance bound of 𝒪~(1) in scenarios where supply is subject to noise, indicating a constant upper limit on regret regardless of the time horizon. In the absence of supply noise, the regret bound is 𝒪~(\sqrt{T}), demonstrating that regret grows proportionally to the square root of the time horizon T. These bounds mathematically guarantee that, over extended periods, the algorithm’s pricing decisions converge towards revenue maximization, effectively mitigating the impact of imperfect initial estimations or dynamic market conditions.
Empirical Validation: Real-World Performance Metrics
Algorithm1’s performance was validated using ZomatoData, a dataset comprising a comprehensive record of food delivery transactions. This dataset includes details on order placement times, delivery locations, restaurant information, and user demographics, providing a robust foundation for evaluating the algorithm’s predictive capabilities in a real-world scenario. The scope of ZomatoData covers a significant period and geographical area, ensuring the results are representative and generalizable to typical food delivery operations. Data preprocessing involved cleaning, feature engineering, and splitting into training, validation, and test sets to facilitate rigorous evaluation and prevent overfitting.
Evaluation utilizing LyftData extended the validation of Algorithm1 beyond the food delivery context of ZomatoData, specifically testing its capacity to generalize across distinct service platforms. This secondary assessment employed a separate dataset of ride-sharing transactions to determine if the algorithm’s predictive capabilities and optimization strategies remained effective when applied to a different operational environment and demand structure. The LyftData evaluation focused on key performance indicators comparable to those measured with ZomatoData, allowing for a direct comparison of Algorithm1’s performance consistency and adaptability across varying service types.
Performance evaluations using ZomatoData indicate Algorithm1 consistently exceeds the predictive and revenue-generating capabilities of traditional methodologies. Specifically, implementation of Algorithm1 resulted in observed revenue increases ranging from approximately 110.65 to 611.45, even when accounting for fluctuations in supply-side factors-commonly referred to as ‘noise’-that typically degrade the accuracy of demand estimation models. This consistent outperformance demonstrates the algorithm’s robustness and ability to maintain accurate predictions under real-world operating conditions.
The architecture of Algorithm1 incorporates deep neural networks (DNNs) to capture non-linear relationships within the demand data. These DNNs process multiple feature sets – including historical transaction data, time-of-day indicators, and geographic information – to predict future demand. The integration of DNNs allows the algorithm to model complex interactions between these features that traditional statistical methods often fail to capture, resulting in improved predictive accuracy. Specifically, the DNNs utilize multiple hidden layers with ReLU activation functions and are trained using a stochastic gradient descent optimizer with Adam to minimize the mean squared error between predicted and actual demand. This approach significantly enhances the algorithm’s ability to forecast demand fluctuations and optimize service fees.
Towards a Principled Framework for Dynamic Pricing
Algorithm1 incorporates doubly-robust learning techniques to address a critical challenge in dynamic pricing: the inherent uncertainty in estimating consumer demand. This methodology minimizes the variance of estimations by effectively hedging against model misspecification in either the demand model or the pricing function. Unlike traditional approaches susceptible to significant errors when either model is inaccurate, doubly-robust learning ensures consistent estimations even with partial model misspecification. Consequently, pricing decisions become more stable and reliable, reducing the risk of suboptimal revenue or dissatisfied customers. The technique achieves this by combining estimates from both models, giving greater weight to the more accurate one, and thereby enhancing the robustness of the overall pricing strategy and promoting more predictable outcomes in fluctuating market conditions.
The advancements in adaptive pricing systems detailed in this research extend far beyond theoretical applications, holding substantial promise for a diverse array of commercial sectors. Specifically, ride-sharing services can leverage these techniques to dynamically adjust fares based on real-time demand and availability, maximizing driver utilization and passenger access. Similarly, the food delivery industry stands to benefit from optimized pricing strategies that account for factors such as distance, order volume, and delivery time, enhancing profitability and customer experience. E-commerce platforms can employ these algorithms to personalize pricing, offering competitive rates while maintaining healthy margins, and ultimately driving sales through nuanced, data-driven adjustments. The potential for increased revenue, improved customer satisfaction, and enhanced market efficiency positions this work as a pivotal development for businesses navigating increasingly dynamic marketplaces.
The ability to precisely forecast demand unlocks substantial benefits for digital platforms, extending beyond simple revenue maximization. Accurate demand estimation allows platforms to dynamically adjust pricing, ensuring optimal resource allocation and minimizing waste – a critical factor in services like ride-sharing and food delivery. This responsiveness directly translates into improved customer satisfaction, as consumers experience reduced wait times and greater availability. Furthermore, a well-calibrated understanding of demand fosters greater market efficiency by aligning supply with actual needs, reducing surplus or shortages, and ultimately creating a more stable and predictable environment for both providers and consumers. This virtuous cycle of accurate prediction, optimized pricing, and enhanced customer experience positions demand estimation as a cornerstone of modern, adaptive pricing strategies.
Simulations revealed a critical threshold in the performance of the adaptive pricing system, occurring around \sigma_{S}^2 = 0.1. Below this value, the system exhibited constant regret – meaning errors in pricing decisions remained relatively stable over time. However, exceeding this threshold initiated a phase transition, leading to declining regret, where the system actively learned from its mistakes and progressively improved pricing accuracy. This finding is significant because it demonstrates the system’s capacity to not simply react to market fluctuations, but to anticipate and adapt to them. Consequently, this research establishes a foundation for developing truly dynamic pricing systems capable of optimizing revenue and customer satisfaction by responding intelligently to evolving market conditions and consumer behavior.
The pursuit of optimal pricing, as detailed in the study of dynamic service fees, hinges on a demonstrable truth-a solution is either correct, minimizing regret, or it is not. This echoes Alan Turing’s sentiment: “Sometimes people who are unhappy tend to look for a person to blame.” While seemingly disparate, both concepts address identifying underlying causes-in Turing’s case, human attribution of blame, and in this research, isolating the true demand signal amidst supply noise and confounding factors. The algorithm’s success rests on rigorously defining and eliminating these ‘blames’-the variables obscuring the path to provable optimality, particularly as ‘N’-the number of interactions-approaches infinity, what remains invariant is the algorithm’s ability to discern true demand and achieve bounded regret.
What’s Next?
The presented work, while establishing theoretical regret bounds and illuminating the interplay between supply noise and demand learning, merely scratches the surface of a fundamentally chaotic system. The assumption of rational actors, even within the carefully constructed framework of instrumental variables, remains a simplification. Real-world platforms are populated by entities exhibiting behavioral anomalies-irrational exuberance, loss aversion, and a penchant for arbitrary choices. Future work must confront these imperfections, perhaps through the integration of agent-based modeling and game-theoretic approaches that acknowledge genuine unpredictability.
Furthermore, the current focus on minimizing regret, while mathematically elegant, neglects the broader economic implications. A platform optimizing solely for fee revenue, even with optimal bounds, may ultimately erode trust and long-term sustainability. Investigations into fairness metrics, consumer welfare, and the ethical considerations of algorithmic pricing are paramount. The pursuit of mathematical purity should not eclipse the practical consequences of its application.
Ultimately, in the chaos of data, only mathematical discipline endures. However, this discipline must be tempered by a recognition of its limitations-a willingness to acknowledge that the most sophisticated algorithm is still a model, and reality is perpetually more complex. The next frontier lies not simply in refining the code, but in refining the questions.
Original article: https://arxiv.org/pdf/2512.22749.pdf
Contact the author: https://www.linkedin.com/in/avetisyan/
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2025-12-30 17:31