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Efficiency of the First-Price Auction in the Autobidding World

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Yuan Deng et el.

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TL;DR
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Online advertising increasingly relies on autobidding, where automated agents manage ad auctions for advertisers. This paper investigates the efficiency of first-price auctions—a dominant format—within this autobidding context. A critical issue is the impact of various bidder types, including traditional utility maximizers and value maximizers (autobidders) who aim to maximize their value subject to return-on-investment (ROI) constraints. Previous research on first-price auctions largely focused on traditional bidders, leaving a gap in understanding autobidding scenarios.

This paper bridges that gap by rigorously analyzing the price of anarchy (PoA) in first-price auctions under full and mixed autobidding environments. The researchers prove a PoA of 1/2 in the full autobidding world and show that in mixed autobidding settings, the PoA degrades to approximately 0.457. Furthermore, the study introduces a machine-learned advice mechanism which significantly improves the efficiency of the auctions, showing that incorporating machine learning can effectively mitigate the negative effects of autobidding. Their findings have significant implications for auction design and automated bidding strategies in online ad markets.

Key Takeaways
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Why does it matter?
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This paper is crucial for researchers in auction theory and online advertising. It significantly advances our understanding of first-price auctions in the context of autobidding, a dominant practice in online advertising. By analyzing price of anarchy (PoA) with different bidder types, the research provides valuable insights for designing more efficient and fair auction mechanisms. The findings are also highly relevant to the ongoing shift towards first-price auctions in online ad markets, guiding the development of better automated bidding strategies and algorithms.


Visual Insights
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This figure shows how the price of anarchy (PoA) in a first-price auction changes based on the accuracy of machine-learned reserves. The x-axis represents the accuracy (Îł) of the reserves, ranging from 0 (completely inaccurate) to 1 (perfectly accurate). The y-axis shows the PoA, which measures the efficiency of the auction. As the accuracy of the reserves increases, the PoA improves, approaching 1 (perfect efficiency). The curve demonstrates a smooth transition between the case with no machine learning (Îł = 0) and perfect accuracy (Îł = 1).

This table summarizes the Price of Anarchy (PoA) for both second-price and first-price auctions under three different bidding scenarios: full autobidding (only value maximizers), mixed autobidding (both value and utility maximizers), and no autobidding (only utility maximizers). The PoA measures the inefficiency of the auction outcome compared to the socially optimal outcome. The table shows that the PoA is significantly lower for first-price auctions in the autobidding world compared to the second-price auction, especially when both types of bidders are present.

Full paper
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