We study local pure coordination games on finite social networks, continuing the framework of Hutchcroft, Rospuskova, and Tamuz. They showed that low inefficiency in local coordination forces the underlying graph to be amenable, with a square-root loss in the amenability parameter. We improve this loss in the binary unbiased setting. Using Shapley values of a mutual-information game associated with the players' local outputs, we prove that if the average disagreement is at most $\varepsilon$, then the graph is $(O(\varepsilon\log(1/\varepsilon)),r)$-amenable. This gives a sharper quantitative converse between local coordination and graph amenability.

翻译：我们研究有限社交网络上的局部纯协调博弈，延续Hutchcroft、Rospuskova和Tamuz的框架。他们表明，局部协调中低效率会迫使底层图具有宽容性，且宽容度参数存在平方根损失。我们在二元无偏设定下改进了这一损失。利用与参与者局部输出相关的互信息博弈的Shapley值，我们证明若平均分歧不超过$\varepsilon$，则该图是$(O(\varepsilon\log(1/\varepsilon)),r)$-宽容的。这给出了局部协调与图宽容性之间更精确的定量逆关系。