The paper designs revenue-maximizing auction mechanisms for agents who aim to maximize their total obtained values rather than the classical quasi-linear utilities. Several models have been proposed to capture the behaviors of such agents in the literature. In the paper, we consider the model where agents are subject to budget and return-on-spend constraints. The budget constraint of an agent limits the maximum payment she can afford, while the return-on-spend constraint means that the ratio of the total obtained value (return) to the total payment (spend) cannot be lower than the targeted bar set by the agent. The problem was first coined by [Balseiro et al., EC 2022]. In their work, only Bayesian mechanisms were considered. We initiate the study of the problem in the worst-case model and compare the revenue of our mechanisms to an offline optimal solution, the most ambitious benchmark. The paper distinguishes two main auction settings based on the accessibility of agents' information: fully private and partially private. In the fully private setting, an agent's valuation, budget, and target bar are all private. We show that if agents are unit-demand, constant approximation mechanisms can be obtained; while for additive agents, there exists a mechanism that achieves a constant approximation ratio under a large market assumption. The partially private setting is the setting considered in the previous work [Balseiro et al., EC 2022] where only the agents' target bars are private. We show that in this setting, the approximation ratio of the single-item auction can be further improved, and a $\Omega(1/\sqrt{n})$-approximation mechanism can be derived for additive agents.

翻译：本文针对以最大化总获取价值为目标（而非经典拟线性效用）的智能体，设计了收益最大化的拍卖机制。现有文献已提出多种模型来刻画此类智能体的行为。本文考虑智能体同时受预算约束与支出回报率约束的模型：预算约束限制智能体可承担的最大支付额；支出回报率约束则要求总获取价值（回报）与总支付（支出）之比不得低于智能体设定的目标阈值。该问题最初由[Balseiro等, EC 2022]提出，但该研究仅考虑了贝叶斯机制。本文首次在最坏情形模型下研究该问题，并将所提机制与离线最优解（最具雄心基准）进行收益比较。根据智能体信息的可获取性，本文区分两种主要拍卖场景：完全私有与部分私有。在完全私有场景中，智能体的估值、预算及目标阈值均为私有信息。我们证明：若智能体为单位需求型，则可获得常数近似机制；而对于可加型智能体，在大市场假设下存在一种实现常数近似比的机制。部分私有场景则是此前研究[Balseiro等, EC 2022]所考虑的设定，仅智能体的目标阈值为私有信息。我们证明在此场景下，单物品拍卖的近似比可进一步提升，且对于可加型智能体可导出$\Omega(1/\sqrt{n})$近似比机制。