The Price of Stability for First Price Auction
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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 ⊊ Bayes Correlated Equilibrium ⊊ Bayes Coarse Correlated Equilibrium ∙ Bayes Nash Equilibrium: For independent valuations, the tight PoS is 1 - 1/ e^2≈ 0.8647, matching the counterpart Price of Anarchy (PoA) bound <cit.>. For correlated valuations, the tight is 1 - 1 / e ≈ 0.6321, matching the counterpart PoA bound <cit.>. This result indicates that, in the worst cases, efficiency degradation depends not on different selections among Bayes Nash Equilibria. ∙ 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 <cit.>. This result indicates that First Price Auctions can be fully efficient when we allow the more general equilibrium concepts.
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