Tree polymatrix games are ppad-hard
arXiv preprint arXiv:2002.12119, 2020•arxiv.org
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 $\epsilon $-fixed point of a 2D LinearFIXP instance, when
$\epsilon $ 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 …
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 $\epsilon $-fixed point of a 2D LinearFIXP instance, when
$\epsilon $ 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 …
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 -fixed point of a 2D LinearFIXP instance, when is any constant less than . This lifts the hardness regime from polynomially small approximations in -dimensions to constant approximations in two-dimensions, and our constant is substantial when compared to the trivial upper bound of .
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