通过价值最大化下的预算和RoS约束进行市场清价机制设计
Mechanism Design via Market Clearing-Prices for Value Maximizers under Budget and RoS Constraints
AI总结：
本文提出了一种在预算和RoS约束下通过市场清价机制实现价值最大化，并证明其在激励相容性和收益近似方面的有效性。
摘要：
在线广告领域向自动出价的转变，使拍卖理论的研究重点从准线性效用最大化转向在财务约束下进行价值最大化。我们研究了具有私人预算和私人支出回报率（RoS）约束的买家的机制设计，但具有公共估值，这一设定受到现代广告平台的启发，其中估值通过机器学习模型进行预测。我们引入了扩展的艾森伯格-加勒程序，一种凸优化框架，扩展以纳入RoS约束。我们证明了该程序的解是唯一的，并且刻画了市场竞争均衡。基于这一理论分析，我们设计了一个市场清价机制，并证明了两个关键性质：（1）它在财务约束方面具有激励相容性，使诚实报告成为最优策略；（2）它实现了第一最佳收益基准的紧致1/2近似，无论是否存在激励相容性。最后，为了实现实际应用，我们提出了一个去中心化的在线算法。忽略对数因子，我们证明在该算法下，卖方的收益和每个买家的效用在m次拍卖中收敛到均衡基准，具有子线性遗憾$\tilde{O}(\sqrt{m})$。
英文摘要：
The transition to auto-bidding in online advertising has shifted the focus of auction theory from quasi-linear utility maximization to value maximization subject to financial constraints. We study mechanism design for buyers with private budgets and private Return-on-Spend (RoS) constraints, but public valuations, a setting motivated by modern advertising platforms where valuations are predicted via machine learning models. We introduce the extended Eisenberg-Gale program, a convex optimization framework generalized to incorporate RoS constraints. We demonstrate that the solution to this program is unique and characterizes the market's competitive equilibrium. Based on this theoretical analysis, we design a market-clearing mechanism and prove two key properties: (1) it is incentive-compatible with respect to financial constraints, making truthful reporting the optimal strategy; and (2) it achieves a tight 1/2-approximation of the first-best revenue benchmark, the maximum revenue of any feasible mechanism, regardless of IC. Finally, to enable practical implementation, we present a decentralized online algorithm. Ignoring logarithmic factors, we prove that under this algorithm, both the seller's revenue and each buyer's utility converge to the equilibrium benchmarks with a sublinear regret of $\tilde{O}(\sqrt{m})$ over $m$ auctions.
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