# Efficiency of Proportional Mechanisms in Online Auto-Bidding Advertising

arXiv: https://arxiv.org/abs/2604.12799 · HTML: https://mlsanity.com/paper/2604.12799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 21 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 11 of 11)

- [Auto-bidding and Auctions in Online Advertising: A Survey](https://mlsanity.com/paper/2408.07685/) (2024)
- [Robust Auction Design in the Auto-bidding World](https://mlsanity.com/paper/2111.02468/) (2021)
- [Autobidders with Budget and ROI Constraints: Efficiency, Regret, and Pacing Dynamics](https://mlsanity.com/paper/2301.13306/) (2023)
- [Budget Pacing in Repeated Auctions: Regret and Efficiency without Convergence](https://mlsanity.com/paper/2205.08674/) (2022)
- [Auction Design in an Auto-bidding Setting: Randomization Improves Efficiency Beyond VCG](https://mlsanity.com/paper/2204.10956/) (2022)
- [Efficiency of the First-Price Auction in the Autobidding World](https://mlsanity.com/paper/2208.10650/) (2022)
- [Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions](https://mlsanity.com/paper/2210.07502/) (2022)
- [Welfare guarantees for proportional allocations](https://mlsanity.com/paper/1402.3447/) (2014)
- [Efficiency of Non-Truthful Auctions in Auto-bidding with Budget Constraints](https://mlsanity.com/paper/2310.09271/) (2023)
- [On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources](https://mlsanity.com/paper/1507.07011/) (2015)
- [The efficiency of resource allocation mechanisms for budget-constrained users](https://mlsanity.com/paper/1707.03551/) (2017)

## Abstract (arXiv)

The rise of automated bidding strategies in online advertising presents new challenges in designing and analyzing efficient auction mechanisms. In this paper, we focus on proportional mechanisms within the context of auto-bidding and study the efficiency of pure Nash equilibria, specifically the price of anarchy (PoA), under the liquid welfare objective. We first establish a tight PoA bound of 2 for the standard proportional mechanism. Next, we introduce a modified version with an alternative payment scheme that achieves a PoA bound of 1 + fracO(1)n-1 where n ≥ 2 denotes the number of bidding agents. This improvement surpasses the existing PoA barrier of 2 and approaches full efficiency as the number of agents increases. Our methodology leverages duality and the Karush-Kuhn-Tucker (KKT) conditions from linear and convex programming. Due to its conceptual simplicity, our approach may offer broader applications for establishing PoA bounds.