# Efficiency of the First-Price Auction in the Autobidding World

arXiv: https://arxiv.org/abs/2208.10650 · HTML: https://mlsanity.com/paper/2208.10650/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Aug 2022.

## Built on by (most cited first, 6 of 6)

- [Multi-channel Autobidding with Budget and ROI Constraints](https://mlsanity.com/paper/2302.01523/) (2023)
- [Multi-Platform Budget Management in Ad Markets with Non-IC Auctions](https://mlsanity.com/paper/2306.07352/) (2023)
- [Online Ad Procurement in Non-stationary Autobidding Worlds](https://mlsanity.com/paper/2307.05698/) (2023)
- [Large-Scale Auto-bidding with Nash Equilibrium Constraints](https://mlsanity.com/paper/2503.10304/) (2025)
- [Smart Fast Finish: Preventing Overdelivery via Daily Budget Pacing at DoorDash](https://mlsanity.com/paper/2509.07929/) (2025)
- [Efficiency of Proportional Mechanisms in Online Auto-Bidding Advertising](https://mlsanity.com/paper/2604.12799/) (2026)

## Abstract (arXiv)

We study the price of anarchy of the first-price auction in the autobidding world, where bidders can be either utility maximizers (i.e., traditional bidders) or value maximizers (i.e., autobidders). We show that with autobidders only, the price of anarchy of the first-price auction is 1/2, and with both kinds of bidders, the price of anarchy degrades to about 0.457 (the precise number is given by an optimization). These results complement the recent result by Jin and Lu [2022] showing that the price of anarchy of the first-price auction with traditional bidders only is 1 - 1/e2. We further investigate a setting where the seller can utilize machine-learned advice to improve the efficiency of the auctions. There, we show that as the accuracy of the advice increases, the price of anarchy improves smoothly from about 0.457 to 1.