  This paper shows the existence of $\mathcal{O}(\frac{1}{n^\gamma})$-Nash
equilibria in $n$-player noncooperative sum-aggregative games in which the
players' cost functions, depending only on their own action and the average of
all players' actions, are lower semicontinuous in the former while
$\gamma$-H\"{o}lder continuous in the latter. Neither the action sets nor the
cost functions need to be convex. For an important class of sum-aggregative
games, which includes congestion games with $\gamma$ equal to 1, a
gradient-proximal algorithm is used to construct
$\mathcal{O}(\frac{1}{n})$-Nash equilibria with at most $\mathcal{O}(n^3)$
iterations. These results are applied to a numerical example concerning the
demand-side management of an electricity system. The asymptotic performance of
the algorithm when $n$ tends to infinity is illustrated.
