1.283 价格无政府界：重复虚拟第一价格拍卖

中文摘要 AI 辅助

我们研究了在 $n$ 个策略性玩家之间重复分配单一不可分割资源的问题。每个玩家 $i$ 拥有一个私下已知的价值分布 $D_i$，且各玩家及各时期的价值独立抽取。目标是寻找公平且高效的机制。我们应用了具有相等虚拟货币初始禀赋的重复第一价格拍卖。我们证明，每个玩家都能渐近地获得与 Csóka 2026 中相同的公平底线保证 $f(D_i)$；因此，该机制是 $1.283$-最优的。这为这一特殊情况提供了一种更简单且更稳健的替代机制，并可能有助于推导出更尖锐的价格无政府上界。

英文摘要

We study the repeated allocation of a single indivisible resource among $n$ strategic players. Each player $i$ has a privately known value distribution $D_i$, and values are drawn independently across players and periods. The goal is to find fair and efficient mechanisms. We apply the repeated first-price auction with equal initial endowments of virtual money. We show that each player can asymptotically secure the same fair-floor guarantee $f(D_i)$ as in Csóka 2026; consequently, the mechanism is $1.283$-optimal. This provides a simpler and more robust alternative mechanism for this special case and may also help derive sharper upper bounds on the price of anarchy.

发表机构

• Alfréd Rényi Institute of Mathematics（阿尔弗雷德·雷尼数学研究所）

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