[Fnoord]

Yes, either start with always attack, or always retreat.

Another (practical) solution could be to spoof a message, making it appear as if from Eve. Some kind of steganography might work as well (or alternative forms of communication such as pigeons or smoke signals). And if all communications between Alice and Bob is discarded, this would worry either one of them to send a personal messenger who is human. This person could be captured and tortured, sure. But if they get "burned" as well, that'd be an act of war. Plus, if they are able to predetermine that if they don't hear from each other after X time, they attack after X + Y time (e.g. 3 months and 1 month [to prepare]) then the problem can be solved. If they cannot create a clear way of predetermined action based on actions then they'll always retreat.

Actually now that I gave it some further thought this "two general problem" can be observed in the cold war as well via (the nuclear threat of both parties). The nuclear threat from both sides created an equilibrium akin to what could happen in the described situation.