论文标题
树多头式游戏是ppad-hard
Tree Polymatrix Games are PPAD-hard
论文作者
论文摘要
我们证明，在树多蛋白酶游戏中计算NASH平衡是ppad-hard，每个玩家二十个动作。这是一个游戏的第一个PPAD硬度结果，该游戏的每个播放器数量持续数量的互动图是无环的。一路上，我们显示了2D LinearFixp实例的$ε$固定点的ppad-hard，当$ε$的常数是小于$（\ sqrt {2} -1）/2 \ of 0.2071 $时。这将硬度制度从$ k $维度的多项式小近似值到二维的常数近似值，与$ 0.5 $的琐碎上限相比，我们的常数很大。
We prove that it is PPAD-hard to compute a Nash equilibrium in a tree polymatrix game with twenty actions per player. This is the first PPAD hardness result for a game with a constant number of actions per player where the interaction graph is acyclic. Along the way we show PPAD-hardness for finding an $ε$-fixed point of a 2D LinearFIXP instance, when $ε$ is any constant less than $(\sqrt{2} - 1)/2 \approx 0.2071$. This lifts the hardness regime from polynomially small approximations in $k$-dimensions to constant approximations in two-dimensions, and our constant is substantial when compared to the trivial upper bound of $0.5$.
