An efficiency ordering of k-price auctions under complete information

Sumit Goel; Jeffrey Zeidel

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arXiv · 2507.05738

An efficiency ordering of k-price auctions under complete information

Sumit Goel·Jeffrey Zeidel

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Abstract

We study $k$-price auctions in a complete information environment and characterize all pure-strategy Nash equilibrium outcomes. In a setting with $n$ agents having ordered valuations, we show that any agent, except those with the lowest $k-2$ valuations, can win in equilibrium. As a consequence, worst-case welfare increases monotonically as we go from $k=2$ (second-price auction) to $k=n$ (lowest-price auction), with the first-price auction achieving the highest worst-case welfare.

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Sumit Goel, Jeffrey Zeidel. 2025-07-08. An efficiency ordering of k-price auctions under complete information. https://arxiv.org/abs/2507.05738

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