自动竞价拍卖的PPAD硬度之外
Beyond the PPAD hardness of Auto-bidding Auctions
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中文总结 AI 辅助
针对自动竞价拍卖最坏情况均衡计算的PPAD完全性与实际收敛性的矛盾，引入弥散分析框架，提出具线性收敛性的GNE求解器，其复杂度匹配现实市场表现，且涵盖两类特例。
中文摘要 AI 辅助
计算特定自动竞价均衡在最坏情况下是PPAD完全问题，但此类实例在现实中极少出现——现实里采用简单分散式学习策略的广告主通常能快速收敛。我们证明这并不矛盾：该硬度要求原子性，当价值分布为非原子性（现实市场中正是如此）时硬度消失。为衔接最坏情况硬度与实际收敛性，我们引入弥散分析，这是一种研究竞价者价值来自一般非原子分布时均衡计算的最坏情况之外框架。在此框架下，自动竞价均衡成为可分离单调的广义纳什均衡（GNE）。针对该GNE，我们给出首个具有最后迭代线性收敛性的求解器，因此该均衡具有多项式弥散复杂度，与现实市场中观察到的收敛性匹配。具体而言，当支付规则是首价与次价的凸组合时，我们的框架将预算 pacing 和 throttling 均衡作为特例包含在内。
英文摘要
Computing certain autobidding equilibria is PPAD complete in the worst case. Yet such instances rarely arise in practice, where advertisers running simple, decentralized learning strategies usually converge quickly. We show there is no contradiction: the hardness requires atomicity and vanishes once the value distribution is nonatomic, as it is in real world markets. To bridge worst case hardness and practical convergence, we introduce diffuse analysis, a beyond worst case framework that studies equilibrium computation when bidder values are drawn from general nonatomic distributions. Under this framework, the autobidding equilibrium becomes a separately monotone generalized Nash equilibrium (GNE). For this GNE, we give the first solver with last iterate linear convergence. Thus, the equilibrium has polynomial diffuse complexity, matching the convergence observed in real-world markets. Concretely, our framework subsumes the budget pacing and the throttling equilibrium as special cases when the payment rule is a convex combination of first and second price.
