  We study a multi-leader single-follower congestion game where multiple users
(leaders) choose one resource out of a set of resources and, after observing
the realized loads, an adversary (single-follower) attacks the resources with
maximum loads, causing additional costs for the leaders. For the resulting
strategic game among the leaders, we show that pure Nash equilibria may fail to
exist and therefore, we consider approximate equilibria instead. As our first
main result, we show that the existence of a $K$-approximate equilibrium can
always be guaranteed, where $K \approx 1.1974$ is the unique solution of a
cubic polynomial equation. To this end, we give a polynomial time combinatorial
algorithm which computes a $K$-approximate equilibrium. The factor $K$ is
tight, meaning that there is an instance that does not admit an
$\alpha$-approximate equilibrium for any $\alpha<K$. Thus $\alpha=K$ is the
smallest possible value of $\alpha$ such that the existence of an
$\alpha$-approximate equilibrium can be guaranteed for any instance of the
considered game. Secondly, we focus on approximate equilibria of a given fixed
instance. We show how to compute efficiently a best approximate equilibrium,
that is, with smallest possible $\alpha$ among all $\alpha$-approximate
equilibria of the given instance.
