I don’t think Austria-Hungry was in a prisoners’ dilemma as they wanted a war so long as they would have German support. I think the Prisoners’ dilemma (imperfectly) comes into play for Germany, Russia, and then France given that Germany felt it needed to have Austria-Hungry as a long-term ally or risk getting crushed by France + Russia in some future war.
I don’t think Austria-Hungry was in a prisoners’ dilemma as they wanted a war so long as they would have German support. I think the Prisoners’ dilemma (imperfectly) comes into play for Germany, Russia, and then France given that Germany felt it needed to have Austria-Hungry as a long-term ally or risk getting crushed by France + Russia in some future war.