We study the design of prior-independent auctions in a setting with heterogeneous bidders. In particular, we consider the setting of selling to $n$ bidders whose values are drawn from $n$ independent but not necessarily identical distributions. We work in the robust auction design regime, where we assume the seller has no knowledge of the bidders' value distributions and must design a mechanism that is prior-independent. While there have been many strong results on prior-independent auction design in the i.i.d. setting, not much is known for the heterogeneous setting, even though the latter is of significant practical importance. Unfortunately, no prior-independent mechanism can hope to always guarantee any approximation to Myerson's revenue in the heterogeneous setting; similarly, no prior-independent mechanism can consistently do better than the second-price auction. In light of this, we design a family of (parametrized) randomized auctions which approximates at least one of these benchmarks: For heterogeneous bidders with regular value distributions, our mechanisms either achieve a good approximation of the expected revenue of an optimal mechanism (which knows the bidders' distributions) or exceeds that of the second-price auction by a certain multiplicative factor. The factor in the latter case naturally trades off with the approximation ratio of the former case. We show that our mechanism is optimal for such a trade-off between the two cases by establishing a matching lower bound. Our result extends to selling $k$ identical items to heterogeneous bidders with an additional $O\big(\ln^2 k\big)$-factor in our trade-off between the two cases.

翻译：我们研究异质投标者场景下的先验无关拍卖设计。具体而言，考虑向$n$个投标者进行拍卖的情形，其估值分别服从$n$个独立但未必相同的分布。我们在稳健拍卖设计框架下开展工作，假设卖方完全不知晓投标者的估值分布，必须设计一个先验无关的机制。尽管独立同分布场景下的先验无关拍卖设计已取得诸多重要成果，但在具有重要实践意义的异质场景中仍鲜有进展。不幸的是，在异质场景下，任何先验无关机制都无法保证始终接近迈尔森最优收益的某个近似比；同样，没有任何先验无关机制能持续超越第二价格拍卖。基于此，我们设计了一族（参数化的）随机拍卖机制，能够逼近至少其中一个基准：对于具有规则估值分布的异质投标者，我们的机制要么能对最优机制（已知投标者分布）的期望收益实现良好近似，要么能以特定乘法因子超越第二价格拍卖。后者的因子会自然与前者的近似比形成权衡。通过建立匹配的下界，我们证明了该机制在此类权衡中的最优性。我们的结果可推广至向异质投标者销售$k$个相同物品的场景，此时两个基准间的权衡因子将额外增加$O\big(\ln^2 k\big)$倍。