We complete the characterization of the computational complexity of equilibrium in public goods games on graphs by proving that the problem is NP-complete for every finite non-monotone best-response pattern. This answers the open problem of [Gilboa and Nisan, 2022], and completes the answer to a question raised by [Papadimitriou and Peng, 2021], for all finite best-response patterns.

翻译：我们通过证明对于每个有限非单调最佳响应模式，该问题都是NP完全的，从而完成了图上公共物品博弈中均衡计算复杂性的刻画。这一结果解答了[Gilboa和Nisan，2022]提出的开放问题，并完整回应了[Papadimitriou和Peng，2021]针对所有有限最佳响应模式所提出的疑问。