We prove that computing an $ε$-approximate Nash equilibrium of a win-lose bimatrix game with constant sparsity is PPAD-hard for inverse-polynomial $ε$. Our result holds for 3-sparse games, which is tight given that 2-sparse win-lose bimatrix games can be solved in polynomial time.

翻译：我们证明了计算具有常数稀疏度的输赢双矩阵博弈的$ε$-近似纳什均衡对于逆多项式$ε$是PPAD难的。我们的结果对3-稀疏博弈成立，这一结论是紧的，因为2-稀疏输赢双矩阵博弈可在多项式时间内求解。