  Security is a subject of increasing attention in our actual society in order
to protect critical resources from information disclosure, theft or damage. The
informal model of attack trees introduced by Schneier, and widespread in the
industry, is advocated in the 2008 NATO report to govern the evaluation of the
threat in risk analysis. Attack-defense trees have since been the subject of
many theoretical works addressing different formal approaches.
  In 2017, M. Audinot et al. introduced a path semantics over a transition
system for attack trees. Inspired by the later, we propose a two-player
interpretation of the attack-tree formalism. To do so, we replace transition
systems by concurrent game arenas and our associated semantics consist of
strategies. We then show that the emptiness problem, known to be NP-complete
for the path semantics, is now PSPACE-complete. Additionally, we show that the
membership problem is coNP-complete for our two-player interpretation while it
collapses to P in the path semantics.
