The Price of Stability for First Price Auction

This paper establishes the Price of Stability (PoS) for First Price Auctions, for all equilibrium concepts that have been studied in the literature: Bayesian Nash Equilibrium ⊊ Bayesian Correlated Equilibrium ⊊ Bayesian Coarse Correlated Equilibrium. • Bayesian Nash Equilibrium: For independent valuations, the tight PoS is 1 − 1/e2 ≈ 0.8647, matching the counterpart Price of Anarchy (PoA) bound [JL22]. For correlated valuations, the tight PoS is 1 − 1/e ≈ 0.6321, matching the counterpart PoA bound [ST13, Syr14]. This result indicates that, in the worst cases, efficiency degradation depends not on different selections among Bayesian Nash Equilibria. • Bayesian (Coarse) Correlated Equilibrium: For independent or correlated valuations, the tight PoS is always 1 = 100%, i.e., no efficiency degradation. This result indicates that First Price Auctions can be fully efficient when we allow the more general equilibrium concepts. * The full version of the paper can be accessed at https://arxiv.org/abs/2207.04455