  The guarding game is a game in which several cops try to guard a region in a
(directed or undirected) graph against Robber. Robber and the cops are placed
on the vertices of the graph; they take turns in moving to adjacent vertices
(or staying), cops inside the guarded region, Robber on the remaining vertices
(the robber-region). The goal of Robber is to enter the guarded region at a
vertex with no cop on it. The problem is to determine whether for a given graph
and given number of cops the cops are able to prevent Robber from entering the
guarded region. Fomin et al. [Fomin, Golovach, Hall, Mihalak, Vicari, Widmayer:
How to Guard a Graph? Algorithmica 61(4), 839--856 (2011)] proved that the
problem is NP-complete when the robber-region is restricted to a tree. Further
they prove that is it PSPACE-complete when the robber-region is restricted to a
directed acyclic graph, and they ask about the problem complexity for arbitrary
graphs. In this paper we prove that the problem is E-complete for arbitrary
directed graphs.
