论文标题
首价拍卖的稳定价格
The Price of Stability for First Price Auction
论文作者
论文摘要
本文确定了第一次价格拍卖的稳定价格（POS），对于文献中已经研究的所有均衡概念：贝叶斯nash均衡$ \ subsetneq $ bayes bayes bayes相关均衡$ \ subsetneq $ subsetneq $ subsetneq $ $ \ bullet $ bayes nash均衡：对于独立的估值，紧密的pos为$ 1-1/ e^{2} \大约0.8647 $，与无政府状态（POA）绑定\ cite \ cite \ cite {jl22}的对应价格匹配。对于相关的估值，紧密的$ \ pos $为$ 1-1 / e \约0.6321 $，与对应的poa绑定\ cite \ cite {st13，s14}匹配。该结果表明，在最坏的情况下，效率降解并不取决于贝叶斯纳什均衡中的不同选择。 $ \ bullet $贝叶斯粗相关平衡：对于独立或相关的估值，紧密的pos始终为$ 1 = 100 \％$，即没有效率降解，与对应的poa bond $ 1-1 / e \ bount $ 1-1 / e \约0.6321 $ \ cite {st13，s14}。该结果表明，当我们允许更一般的平衡概念时，第一价格拍卖可能是完全有效的。
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.
