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arXiv · 2609.17395

The price of anarchy in the max-distance network creation game is not constant

Christoph Schlegel
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Abstract

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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Christoph Schlegel. 2026-09-15. The price of anarchy in the max-distance network creation game is not constant. https://arxiv.org/abs/2609.17395

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