Simple, Optimal and Efficient Auctions

We study the extent to which simple auctions can simultaneously achieve good revenue and efficiency guarantees in single-item settings. Motivated by the optimality of the second price auction with monopoly reserves when the bidders' values are drawn i.i.d. from regular distributions [12], and its approximate optimality when they are drawn from independent regular distributions [11], we focus our attention to the second price auction with general (not necessarily monopoly) reserve prices, arguably one of the simplest and most intuitive auction formats. As our main result, we show that for a carefully chosen set of reserve prices this auction guarantees at least 20% of both the optimal welfare and the optimal revenue, when the bidders' values are distributed according to independent, not necessarily identical, regular distributions. We also prove a similar guarantee, when the values are drawn i.i.d. from a--possibly irregular--distribution.