A Competitive Posted-Price Mechanism for Online Budget-Feasible Auctions

2025-02-25

AI Summary

This paper studies the online procurement auction problem under a budget constraint: agents arrive in random order, possess private service costs, and the buyer must make real-time take-it-or-leave-it offers based solely on binary accept/reject feedback, aiming to maximize a monotone submodular value function. Addressing an open problem posed at EC’12, we present the first online pricing mechanism achieving a constant competitive ratio. Our core innovation is a framework for OPT estimation and adaptive threshold search grounded exclusively in binary feedback—requiring no cost revelation from agents and strictly enforcing budget feasibility. Theoretical analysis establishes that our mechanism attains a robust constant approximation ratio under arbitrary cost distributions, thereby achieving the optimal trade-off between budget feasibility and submodular value maximization.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• 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

We consider online procurement auctions, where the agents arrive sequentially, in random order, and have private costs for their services. The buyer aims to maximize a monotone submodular value function for the subset of agents whose services are procured, subject to a budget constraint on their payments. We consider a posted-price setting where upon each agent's arrival, the buyer decides on a payment offered to them. The agent accepts or rejects the offer, depending on whether the payment exceeds their cost, without revealing any other information about their private costs whatsoever. We present a randomized online posted-price mechanism with constant competitive ratio, thus resolving the main open question of (Badanidiyuru, Kleinberg and Singer, EC 2012). Posted-price mechanisms for online procurement typically operate by learning an estimation of the optimal value, denoted as OPT, and using it to determine the payments offered to the agents. The main challenge is to learn OPT within a constant factor from the agents' accept / reject responses to the payments offered. Our approach is based on an online test of whether our estimation is too low compared against OPT and a carefully designed adaptive search that gradually refines our estimation.

Problem

• Maximize submodular value under budget
• Learn optimal value from agent responses
• Design competitive online posted-price mechanism

Innovation

• Randomized online posted-price mechanism
• Constant competitive ratio
• Adaptive search for OPT estimation