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arXiv 2310.09271cs.GT
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带预算约束的自动出价中非真实拍卖的效率

Efficiency of Non-Truthful Auctions in Auto-bidding with Budget Constraints

Christopher Liaw, Aranyak Mehta, Wennan Zhu

AI总结:

该研究针对带ROS和预算约束的自动出价场景,分析非真实拍卖的效率,证明FPA是最优确定性机制,还提出两种随机机制突破确定性下界,并揭示统一出价对两类机制效率的相反影响。

摘要:

我们研究了同时受支出回报率(ROS)和预算约束的自动出价器中非真实拍卖的效率。机制的效率由无政府状态价格(PoA)衡量,即任意均衡的流动福利与最优(可能是随机的)分配之间的最坏情况比值。我们的首个主要结果是,在该场景下,第一价格拍卖(FPA)在确定性机制中是最优的。在无任何假设的情况下,FPA的PoA为$n$,我们证明这对任意确定性机制都是紧的。然而,在“出价者对任意查询的价值不超过其总预算”这一温和假设下,我们证明其PoA至多为$2$。该界同样是紧的,因为它与无预算约束时的最优PoA一致。接下来我们分析了两种随机机制:随机FPA(rFPA)和“准比例”FPA。我们证明了两个凸显随机化在该场景中有效性的结果。首先,我们证明在无任何假设的情况下,针对两个出价者的rFPA的PoA至多为$1.8$,这拓展了仅关注ROS约束的先前研究。其次,我们证明准比例FPA在任意数量出价者、无任何假设的情况下PoA为$2$。这两个结果都突破了确定性场景中的下界。最后,我们研究了假设出价者采用统一出价的场景。我们发现,统一出价对确定性机制的效率有害,但对随机机制有益,这与无预算约束的场景形成了鲜明对比。

英文摘要:

We study the efficiency of non-truthful auctions for auto-bidders with both return on spend (ROS) and budget constraints. The efficiency of a mechanism is measured by the price of anarchy (PoA), which is the worst case ratio between the liquid welfare of any equilibrium and the optimal (possibly randomized) allocation. Our first main result is that the first-price auction (FPA) is optimal, among deterministic mechanisms, in this setting. Without any assumptions, the PoA of FPA is $n$ which we prove is tight for any deterministic mechanism. However, under a mild assumption that a bidder's value for any query does not exceed their total budget, we show that the PoA is at most $2$. This bound is also tight as it matches the optimal PoA without a budget constraint. We next analyze two randomized mechanisms: randomized FPA (rFPA) and "quasi-proportional" FPA. We prove two results that highlight the efficacy of randomization in this setting. First, we show that the PoA of rFPA for two bidders is at most $1.8$ without requiring any assumptions. This extends prior work which focused only on an ROS constraint. Second, we show that quasi-proportional FPA has a PoA of $2$ for any number of bidders, without any assumptions. Both of these bypass lower bounds in the deterministic setting. Finally, we study the setting where bidders are assumed to bid uniformly. We show that uniform bidding can be detrimental for efficiency in deterministic mechanisms while being beneficial for randomized mechanisms, which is in stark contrast with the settings without budget constraints.

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