Utility Maximizer or Value Maximizer: Mechanism Design for Mixed Bidders in Online Advertising

TL;DR

This paper designs a truthful auction mechanism for mixed bidders in online advertising, combining utility and value maximizers, achieving near-optimal social welfare approximation.

Contribution

It introduces a novel payment rule that unifies VCG and GSP mechanisms, enabling truthful auction design in mixed bidder environments.

Findings

Achieves a 2-approximation ratio for social welfare.

Proves a lower bound of 1.25 for approximation ratio.

Generalizes classical auction mechanisms for mixed bidder types.

Abstract

Digital advertising constitutes one of the main revenue sources for online platforms. In recent years, some advertisers tend to adopt auto-bidding tools to facilitate advertising performance optimization, making the classical \emph{utility maximizer} model in auction theory not fit well. Some recent studies proposed a new model, called \emph{value maximizer}, for auto-bidding advertisers with return-on-investment (ROI) constraints. However, the model of either utility maximizer or value maximizer could only characterize partial advertisers in real-world advertising platforms. In a mixed environment where utility maximizers and value maximizers coexist, the truthful ad auction design would be challenging since bidders could manipulate both their values and affiliated classes, leading to a multi-parameter mechanism design problem. In this work, we address this issue by proposing a payment rule which combines the corresponding ones in classical VCG and GSP mechanisms in a novel way. Based on this payment rule, we propose a truthful auction mechanism with an approximation ratio of $2$ on social welfare, which is close to the lower bound of at least $\frac{5}{4}$ that we also prove. The designed auction mechanism is a generalization of VCG for utility maximizers and GSP for value maximizers.