Posted Pricing for Online Selection: Limited Price Changes and Risk Sensitivity

2025-12-02

AI Summary

Online resource allocation via posted-price mechanisms (PPMs) faces two key challenges: frequent price adjustments provoke fairness concerns and increase operational costs, while expectation-based performance evaluation neglects risk sensitivity. Method: We introduce the *kSelection-(δ,Δ)* problem class to model online selection under bounded price changes and explicit tail-risk control. We design a single-random-seed–based correlated pricing mechanism that jointly optimizes price-change frequency and risk mitigation by maximizing Conditional Value-at-Risk (CVaR) in adversarial environments. Contribution/Results: We establish a fundamental trade-off between price-change budget and risk sensitivity, proving tight optimality for several special cases. Our mechanism significantly enhances the robustness and tail performance of social welfare—achieving improved worst-case guarantees and reduced vulnerability to distributional uncertainty—while strictly respecting the prescribed limit on price revisions.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

Posted-price mechanisms (PPMs) are a widely adopted strategy for online resource allocation due to their simplicity, intuitive nature, and incentive compatibility. To manage the uncertainty inherent in online settings, PPMs commonly employ dynamically increasing prices. While this adaptive pricing achieves strong performance, it introduces practical challenges: dynamically changing prices can lead to fairness concerns stemming from price discrimination and incur operational costs associated with frequent updates. This paper addresses these issues by investigating posted pricing constrained by a limited, pre-specified number of allowed price changes, denoted by $Delta$. We further extend this framework by incorporating a second critical dimension: risk sensitivity. Instead of evaluating performance based solely on expectation, we utilize a tail-risk objective-specifically, the Conditional Value at Risk (CVaR) of the total social welfare, parameterized by a risk level $delta in [0, 1]$. We formally introduce a novel problem class kSelection-$(delta,Delta)$ in online adversarial selection and propose a correlated PPM that utilizes a single random seed to correlate posted prices. This correlation scheme is designed to address both the limited price changes and simultaneously enhance the tail performance of the online algorithm. Our subsequent analysis provides performance guarantees under these joint constraints, revealing a clear trade-off between the number of allowed price changes and the algorithm's risk sensitivity. We also establish optimality results for several important special cases of the problem.

Problem

• Develops a posted-price mechanism with limited price changes to address fairness and operational costs
• Incorporates risk sensitivity using Conditional Value at Risk to enhance tail performance in social welfare
• Analyzes trade-offs between allowed price changes and risk sensitivity in online adversarial selection

Innovation

• Limited price changes with pre-specified bound
• Risk-sensitive objective using Conditional Value at Risk
• Correlated posted pricing with single random seed