  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.
