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

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 priorindependent 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 single-item auctions for agents with budgets and the objectives of welfare and with a natural regularity assumption on the distribution. Our main results show that the all-pay auction (a non-revelation mechanism) is an optimal prior-independent approximation mechanism. The all-pay auction, however, is not a revelation mechanism. We prove that prior-independent approximation of best revelation mechanism is strictly worse than that of the all-pay auction. Thus, the revelation gap is at least a constant. Finally, we show that the clinching auction (a revelation mechanism) is a prior-independent e ≈ 2.714 approximation. Thus the revelation gap is a constant. Many of our analyses extend to the revenue objective, position environments, and irregular distributions.