  We study public goods games, a type of game where every player has to decide
whether or not to produce a good which is public, i.e., neighboring players can
also benefit from it. Specifically, we consider a setting where the good is
indivisible and where the neighborhood structure is represented by a directed
graph, with the players being the nodes. Papadimitriou and Peng (2023) recently
showed that in this setting computing mixed Nash equilibria is PPAD-hard, and
that this remains the case even for $\varepsilon$-well-supported approximate
equilibria for some sufficiently small constant $\varepsilon$. In this work, we
strengthen this inapproximability result by showing that the problem remains
PPAD-hard for any non-trivial approximation parameter $\varepsilon$.
