发表机构
Criteo AI Lab（Criteo 人工智能实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究探讨平局打破规则对虚拟博弈收敛性的影响，发现标准规则导致不收敛，而修改规则可恢复收敛并达到ε-均衡。
AI 中文摘要
我们研究了在具有独立离散价值和离散投标集的2个投标人、对称一级价格拍卖中的连续时间虚拟博弈。我们首先展示了一个最小实例——两个投标人、两个价值、三个正投标——在该实例上，采用标准均匀分割平局打破规则的虚拟博弈不收敛于对称贝叶斯-纳什均衡：该均衡不稳定，动力学收敛于远离纳什均衡的稳定极限环。然后我们证明，对平局打破规则进行一个小修改——在平局情况下给予每个投标人零收益——恢复了收敛性：虚拟博弈收敛于修改后博弈的纳什均衡。该极限在广泛设置中是原始拍卖的ε-均衡。
英文摘要
We study continuous-time fictitious play in 2-bidder, symmetric first-price auctions with independently distributed discrete values and a discrete bid set. We first exhibit a minimal instance --- two bidders, two values, three positive bids --- on which fictitious play with the standard uniform-split tie-breaking rule does \emph{not} converge to the symmetric Bayes--Nash equilibrium: the equilibrium is unstable and the dynamics converge to a stable limit cycle far from the Nash equilibrium. We then show that a small modification of the tie-breaking rule --- awarding a payoff of zero to every bidder in case of a tie --- restores convergence: fictitious play converges to a Nash equilibrium of the modified game. This limit is an $ε$-equilibrium of the original auction in a broad range of settings.
