Auto-bidding is an area of increasing importance in the domain of online advertising. We study the problem of designing auctions in an auto-bidding setting with the goal of maximizing welfare at system equilibrium. Previous results showed that the price of anarchy (PoA) under VCG is 2 and also that this is tight even with two bidders. This raises an interesting question as to whether VCG yields the best efficiency in this setting, or whether the PoA can be improved upon. We present a prior-free randomized auction in which the PoA is approx. 1.896 for the case of two bidders, proving that one can achieve an efficiency strictly better than that under VCG in this setting. We also provide a stark impossibility result for the problem in general as the number of bidders increases -- we show that no (randomized) anonymous truthful auction can have a PoA strictly better than 2 asymptotically as the number of bidders per query increases. While it was shown in previous work that one can improve on the PoA of 2 if the auction is allowed to use the bidder's values for the queries in addition to the bidder's bids, we note that our randomized auction is prior-free and does not use such additional information; our impossibility result also applies to auctions without additional value information.
翻译:在网上广告领域,自动招标是一个日益重要的领域。我们研究了在自动招标环境下设计拍卖的问题,目的是在系统平衡下最大限度地提高福利。以前的结果显示,在VCG下无政府状态的价格为2,而且即使有两个投标人,这也十分紧张。这提出了一个令人感兴趣的问题,即VCG在这一背景下是否产生最佳效率,或者《行动纲领》能否得到改进。我们提出了一个事先自由随机拍卖,其中《行动纲领》大约为1.896,涉及两个投标人的情况,证明在这种环境下,一个人可以取得比《VCG》下的效率高得多的效率。我们还提供了由于投标人数目增加,一般而言无法产生的问题 -- -- 我们表明,任何(被允许的)匿名真实拍卖都不可能产生严格高于2个单一的效益,因为每次询问的投标人数目会增加。我们以前的工作表明,如果允许拍卖在投标人投标之外使用投标人的价值,那么2号《行动纲领》就能得到改进。我们还注意到,在无风险的情况下,我们也没有使用其他的随机拍卖结果。