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 $1 - 1/ e^{2} \approx 0.8647$, matching the counterpart Price of Anarchy (PoA) bound \cite{JL22}. For correlated valuations, the tight $\PoS$ is $1 - 1 / e \approx 0.6321$, matching the counterpart PoA bound \cite{ST13,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 $1 - 1 / e \approx 0.6321$ \cite{ST13,S14}. This result indicates that First Price Auctions can be fully efficient when we allow the more general equilibrium concepts.
翻译：本文确立了第一次价格拍卖的稳定价格(POS),用于文献中研究的所有均衡概念:Bayes Nash equilibrium $\ subsetneqq$ Bayes 相关平衡 $\ subsetneq$ Bayes coparum $\ subsetneq$ Bayes coquilibrium $\ ballet 0.8647$ 。对于相关估值,紧的美元= POS$ 1 - 1 / e aprox 0.6321$, 与对应的PoA 绑定 {ST13, S14} 。结果显示,在最差的情况下,效率的下降取决于Bayes Nash Equiliblibririar. $\ bulllet $ Bayesian Coarse Cor equiliblium: 对于独立或相关估值,紧凑的POS $13 e e polx lex legal $ 1= e equeal develop.
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