Position Auctions with a Capacity Constraint

2026-05-12

AI Summary

This work addresses the challenge in modern advertising systems where ads of heterogeneous sizes must be jointly selected and allocated under global spatial capacity constraints. The problem is modeled as a capacitated matching problem, for which the authors propose a novel algorithm combining density-first prioritization with capacity-aware local reallocation. They further introduce, for the first time, a randomized mechanism that achieves a constant-factor approximation ratio while being universally truthful. This mechanism overcomes the limitations of traditional greedy approaches by simultaneously respecting spatial capacity constraints and significantly improving social welfare, with rigorous theoretical guarantees on both computational efficiency and incentive compatibility.

Abstract

Sponsored search auctions are commonly modeled as an assignment of a fixed set of slots (positions) to a set of advertisers, with welfare maximization being reducible to a standard matching problem. Motivated by modern ad formats, we study a richer variant of the classical position auctions model, in which ads have heterogeneous sizes and the platform must jointly select and assign a subset of ads to positions subject to a global space constraint. We formulate this as a matching problem with a capacity constraint, and propose an algorithmic technique that goes beyond simple greedy methods while achieving constant factor approximation guarantees. Our allocation rule augments density-based ordering with capacity-aware local improvements, which allow for re-allocations that improve welfare, while respecting the capacity constraint. Applied in the context of position auctions, we analyze this mechanism under the assumption of single-parameter agents and position-dependent click-through-rates (CTRs). We show that a minor modification to our approach yields a universally truthful randomized mechanism with a constant factor approximation guarantee. To the best of our knowledge, this is the first truthful constant-approximation mechanism for this variant of capacity-constrained matching.

Problem

• position auctions
• capacity constraint
• heterogeneous ad sizes
• welfare maximization
• sponsored search

Innovation

• capacity-constrained matching
• position auctions
• truthful mechanism
• constant-factor approximation
• ad allocation