Online Advertising with Spatial Interactions

TL;DR

This paper introduces a new framework for modeling spatial externalities in online advertising, analyzing algorithms for ad allocation that account for proximity effects, and establishing complexity results for different models.

Contribution

It proposes a novel spatial externality model for ad allocation, providing algorithms for certain cases and hardness results for others, advancing understanding of spatial effects in online advertising.

Findings

Polynomial-time algorithm with constant approximation for Nearest-Neighbor model.

Monotone allocation rule that can be implemented as a truthful mechanism.

Strong hardness of approximation for the Product-Distance model.

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.