Generalized Prophet Inequalities for Online Auctions

2026-09-30

AI Summary

This study addresses the limitation of traditional online auctions that frequently overlook budget constraints and heterogeneous agent objectives. By modeling agent goals and budgets as stochastic inputs, this work analyzes the robustness of anonymous pricing mechanisms. It proposes a generalized equilibrium pricing framework to unify hybrid objectives and establishes a reduction from budget-constrained settings to budget-free value maximization. The methodology integrates techniques from stochastic game theory, mechanism design, and competitive ratio analysis. As its primary contribution, the paper proves constant competitive ratios in core scenarios involving subadditive valuations and reveals intrinsic trade-offs in price sensitivity. These findings provide rigorous theoretical foundations for online mechanism design under complex constraints.

Abstract

Prophet Inequalities for online auctions, as many classical auction settings, traditionally consider agents who strive to maximize quasi-linear utility, i.e. their obtained value minus the price paid. This simplified view of the agents' objectives does not capture real-world settings where agents are almost always constrained by budgets, and can have different objectives altogether (e.g., very prominently, value maximizers in autobidding). We generalize classic prophet inequality auction settings to accommodate unknown, varying types of agent objectives and budgets, modeling them as stochastic input similar to the traditional valuation distributions. In this new model, we analyze (anonymous) posted-price mechanisms, one main category of which are the balanced prices central to many auction results in the prophet inequality model. We demonstrate both the resilience and limits of balanced price mechanisms for generalized prophet inequalities with stochastic agent objectives, budgets and valuations: our generalization of the balanced prices framework incorporates budget constraints and mixed objectives. We show constant competitive ratios for some the most central settings, spanning all the way up to agents with subadditive valuation functions. On the way, we establish trade-offs between competitive ratio and agents' price-sensitivity, and give a general reduction from the budgeted setting to budget-free value maximizers.

Problem

• Prophet Inequalities
• Online Auctions
• Budget Constraints
• Agent Objectives
• Posted-Price Mechanisms

Innovation

• Prophet Inequalities
• Online Auctions
• Posted-Price Mechanisms
• Budget Constraints
• Balanced Prices