最大距离网络创建博弈中的无政府状态代价不是常数

中文摘要 AI 辅助

在边价格 $\alpha=1$ 时，我们构造了单边最大距离网络创建博弈的一个无限纯纳什均衡族，其无政府状态代价满足 $\PoA\ge2^{\sqrt{\log_2 n}-O(\log\log n)}$。结合已知上界，这给出了沿构造的种群规模序列的 $2^{\Theta(\sqrt{\log n})}$ 渐近行为。我们将 Lavrov、Loh 和 Messegué 构造的大直径距离均匀图的双重覆盖的每条边细分，并让每个细分顶点购买其两条关联边。距离计算排除了所有有利的单边偏离。这些均衡不是严格的。我们还给出了一个简短证明，表明对于任何多项式衰减的边价格，无政府状态代价是常数。

英文摘要

At edge price $α=1$, we construct an infinite family of pure Nash equilibria of the unilateral max-distance network creation game with $\PoA\ge2^{\sqrt{\log_2 n}-O(\log\log n)}$. Together with the known upper bound, this gives $2^{Θ(\sqrt{\log n})}$ along the constructed sequence of population sizes. We subdivide every edge of the bipartite double cover of a distance-uniform graph with large diameter constructed by Lavrov, Loh and Messegué, and let each subdivision vertex buy its two incident edges. A distance calculation rules out every profitable unilateral deviation. The equilibria are not strict. We also give a short proof that the price of anarchy is constant for every polynomially vanishing edge price.

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