An End-to-end Argument in Mechanism Design (Prior-independent Auctions for Budgeted Agents)

TL;DR

This paper investigates the limitations of revelation mechanisms in prior-independent auction design, showing that non-revelation mechanisms like all-pay auctions can achieve near-optimal welfare, highlighting the importance of non-revelation approaches.

Contribution

It introduces the concept of the revelation gap, quantifies the suboptimality of revelation mechanisms, and demonstrates the optimality of all-pay auctions in certain settings.

Findings

All-pay auctions are Bayesian optimal and prior-independent.

Revelation mechanisms have a lower bound approximation ratio of 1.013.

Clinching auctions achieve approximately 2.714 approximation ratio.

Abstract

This paper considers prior-independent mechanism design, namely identifying a single mechanism that has near optimal performance on every prior distribution. We show that mechanisms with truthtelling equilibria, a.k.a., revelation mechanisms, do not always give optimal prior-independent mechanisms and we define the revelation gap to quantify the non-optimality of revelation mechanisms. This study suggests that it is important to develop a theory for the design of non-revelation mechanisms. Our analysis focuses on welfare maximization in single-item auctions for agents with budgets and a natural regularity assumption on their distribution of values. The all-pay auction (a non-revelation mechanism) is the Bayesian optimal mechanism; as it is prior-independent it is also the prior-independent optimal mechanism (a 1-approximation). We prove a lower bound on the prior-independent approximation of revelation mechanisms of 1.013 and that the clinching auction (a revelation mechanism) is a prior-independent $e \approx 2.714$ approximation. Thus the revelation gap for single-item welfare maximization with public budget agents is in $[1.013, e]$. Some of our analyses extend to the revenue objective, position environments, and irregular distributions.