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On the Complexity of Equilibrium Computation in First-Price Auctions
arXiv - CS - Computer Science and Game Theory Pub Date : 2021-03-04 , DOI: arxiv-2103.03238 Aris Filos-Ratsikas, Yiannis Giannakopoulos, Alexandros Hollender, Philip Lazos, Diogo Poças
arXiv - CS - Computer Science and Game Theory Pub Date : 2021-03-04 , DOI: arxiv-2103.03238 Aris Filos-Ratsikas, Yiannis Giannakopoulos, Alexandros Hollender, Philip Lazos, Diogo Poças
We consider the problem of computing a (pure) Bayes-Nash equilibrium in the
first-price auction with continuous value distributions and discrete bidding
space. We prove that when bidders have independent subjective prior beliefs
about the value distributions of the other bidders, computing an
$\varepsilon$-equilibrium of the auction is PPAD-complete, and computing an
exact equilibrium is FIXP-complete.
中文翻译:
一价拍卖中均衡计算的复杂性
我们考虑在具有连续价值分布和离散投标空间的首次价格拍卖中计算(纯)贝叶斯-纳什均衡的问题。我们证明,当投标人对其他投标人的价值分布具有独立的主观先验信念时,计算拍卖的$ \ varepsilon $-平衡是PPAD完全的,而计算精确的平衡是FIXP-完整的。
更新日期:2021-03-05
中文翻译:
一价拍卖中均衡计算的复杂性
我们考虑在具有连续价值分布和离散投标空间的首次价格拍卖中计算(纯)贝叶斯-纳什均衡的问题。我们证明,当投标人对其他投标人的价值分布具有独立的主观先验信念时,计算拍卖的$ \ varepsilon $-平衡是PPAD完全的,而计算精确的平衡是FIXP-完整的。