Online Advertising with Spatial Interactions

2026-02-12

Technology Category

• Search and Optimization: Adversarial Search
• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges

Abstract

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.

Problem

• spatial externalities
• online advertising
• ad allocation
• attention competition
• metric space

Innovation

• spatial externalities
• online advertising
• truthful mechanism
• approximation algorithm
• metric space