在线拍卖的广义先知不等式

中文摘要 AI 辅助

先知不等式用于在线拍卖，如同许多经典拍卖设置，传统上考虑那些努力最大化拟线性效用（即其获得的价值减去支付的价格）的智能体。这种对智能体目标的简化视图未能捕捉现实世界中的设置，在这些设置中，智能体几乎总是受到预算的约束，并且可能拥有完全不同的目标（例如，非常突出的是，自动出价中的价值最大化者）。我们将经典的先知不等式拍卖设置推广，以适应未知的、变化的智能体目标和预算类型，将它们建模为类似于传统估值分布的随机输入。在这个新模型中，我们分析（匿名的）标价机制，其中主要的一类是平衡价格，这对先知不等式模型中的许多拍卖结果至关重要。我们展示了平衡价格机制在具有随机智能体目标、预算和估值的广义先知不等式中的韧性和局限性：我们对平衡价格框架的推广整合了预算约束和混合目标。我们展示了一些最核心设置中的常数竞争比，涵盖直到具有次加性估值函数的智能体。在此过程中，我们建立了竞争比与智能体价格敏感性之间的权衡，并给出了从有预算设置到无预算价值最大化者的通用归约。

英文摘要

Prophet Inequalities for online auctions, as many classical auction settings, traditionally consider agents who strive to maximize quasi-linear utility, i.e. their obtained value minus the price paid. This simplified view of the agents' objectives does not capture real-world settings where agents are almost always constrained by budgets, and can have different objectives altogether (e.g., very prominently, value maximizers in autobidding). We generalize classic prophet inequality auction settings to accommodate unknown, varying types of agent objectives and budgets, modeling them as stochastic input similar to the traditional valuation distributions. In this new model, we analyze (anonymous) posted-price mechanisms, one main category of which are the balanced prices central to many auction results in the prophet inequality model. We demonstrate both the resilience and limits of balanced price mechanisms for generalized prophet inequalities with stochastic agent objectives, budgets and valuations: our generalization of the balanced prices framework incorporates budget constraints and mixed objectives. We show constant competitive ratios for some the most central settings, spanning all the way up to agents with subadditive valuation functions. On the way, we establish trade-offs between competitive ratio and agents' price-sensitivity, and give a general reduction from the budgeted setting to budget-free value maximizers.

发表机构

• Institute for Logic, Language and Computation, University of Amsterdam（阿姆斯特丹大学逻辑、语言与计算研究所）

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