Online advertising platforms must decide how to allocate multiple ads across limited screen real estate, where each ad's effectiveness depends not only on its own placement but also on nearby ads competing for user attention. Such spatial externalities - arising from proximity, clutter, or crowding - can significantly alter welfare and revenue outcomes, yet existing auction and allocation models typically treat ad slots as independent or ordered along a single dimension. We introduce a new framework for spatial externalities in online advertising, in which the value of an ad depends on both its slot and the configuration of surrounding ads. We model ad slots as points in a metric space, and model an advertiser's value as a function of both their bid and a discount factor determined by the configuration of other displayed ads. Within this framework, we analyze two natural models. For the Nearest-Neighbor model, where the value suppression depends only on the closest neighboring ad, we present a polynomial-time algorithm that achieves a constant approximation for the general case. We show that the allocation rule is monotone and can be implemented as a truthful mechanism. For a structured setting of 2D Euclidean space, we provide a PTAS. In contrast, for the Product-Distance model, where interference is aggregated multiplicatively across all neighbors, we establish a strong (and nearly-tight) hardness of approximation - no polynomial-time algorithm can achieve any polynomial-factor approximation unless P=NP, via a reduction from Max-Independent-Set. Our results provide a foundation for reasoning about spatial externalities in ad allocation and for designing efficient, truthful mechanisms under such interactions.

翻译：在线广告平台必须决定如何在有限的屏幕空间内分配多个广告，其中每个广告的效果不仅取决于其自身的位置，还取决于附近争夺用户注意力的其他广告。这种由邻近性、杂乱性或拥挤性引起的空间外部性会显著改变福利和收入结果，然而现有的拍卖和分配模型通常将广告位视为独立的或沿单一维度排序的。我们引入了一个用于在线广告空间外部性的新框架，其中广告的价值既取决于其所在的广告位，也取决于周围广告的配置。我们将广告位建模为度量空间中的点，并将广告主的价值建模为其出价和由其他展示广告配置决定的折扣因子的函数。在此框架内，我们分析了两种自然模型。对于最近邻模型，其中价值抑制仅取决于最邻近的广告，我们提出了一种多项式时间算法，该算法在一般情况下能达到常数近似比。我们证明了该分配规则是单调的，并且可以实现为一种真实机制。针对二维欧几里得空间的结构化设置，我们提供了一种PTAS。相比之下，对于乘积距离模型，其中干扰在所有邻居间以乘法方式聚合，我们建立了（近乎紧的）强近似困难性——除非P=NP，否则没有多项式时间算法能实现任何多项式因子的近似，这通过从最大独立集问题的归约来证明。我们的结果为推理广告分配中的空间外部性以及在此类交互下设计高效、真实的机制奠定了基础。