Truthfulness with Value-Maximizing Bidders

TL;DR

This paper investigates the limits of truthful auction mechanisms for value-maximizing bidders, showing fundamental bounds on approximation ratios in multi-object settings and proposing improved ratios under certain valuation restrictions.

Contribution

It establishes upper bounds on deterministic truthful approximation ratios and introduces a framework for randomized mechanisms with better ratios, especially for restricted valuations.

Findings

Deterministic truthful mechanisms cannot surpass a 1/n approximation ratio for general valuations.

Randomized mechanisms can achieve an O(√m) approximation ratio.

Better ratios are possible in environments with restricted valuations.

Abstract

In markets such as digital advertising auctions, bidders want to maximize value rather than payoff. This is different to the utility functions typically assumed in auction theory and leads to different strategies and outcomes. We refer to bidders who maximize value as value bidders. While simple single-object auction formats are truthful, standard multi-object auction formats allow for manipulation. It is straightforward to show that there cannot be a truthful and revenue-maximizing deterministic auction mechanism with value bidders and general valuations. Approximation has been used as a means to achieve truthfulness, and we study which approximation ratios we can get from truthful approximation mechanisms. We show that the approximation ratio that can be achieved with a deterministic and truthful approximation mechanism with $n$ bidders and $m$ items cannot be higher than 1/n for general valuations. For randomized approximation mechanisms there is a framework with a ratio of O(sqrt(m)). We provide better ratios for environments with restricted valuations.