# The Price of Stability for First Price Auction

arXiv: https://arxiv.org/abs/2207.04455 · HTML: https://mlsanity.com/paper/2207.04455/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Price of Anarchy of First-Price Auctions in Agentic Markets](https://mlsanity.com/paper/2610.20587/) (2026)

## Abstract (arXiv)

This paper establishes the Price of Stability (PoS) for First Price Auctions, for all equilibrium concepts that have been studied in the literature: Bayes Nash Equilibrium subsetneq Bayes Correlated Equilibrium subsetneq Bayes Coarse Correlated Equilibrium bullet Bayes Nash Equilibrium: For independent valuations, the tight PoS is 1 - 1/ e2 ≈ 0.8647, matching the counterpart Price of Anarchy (PoA) bound citeJL22. For correlated valuations, the tight PoS is 1 - 1 / e ≈ 0.6321, matching the counterpart PoA bound citeST13,S14. This result indicates that, in the worst cases, efficiency degradation depends not on different selections among Bayes Nash Equilibria. bullet Bayesian Coarse Correlated Equilibrium: For independent or correlated valuations, the tight PoS is always 1 = 100%, i.e., no efficiency degradation, different from the counterpart PoA bound 1 - 1 / e ≈ 0.6321 citeST13,S14. This result indicates that First Price Auctions can be fully efficient when we allow the more general equilibrium concepts.