If you know that at least one message from Alice goes through, and Alice says "do this with priority 0", then yes, you can solve the problem. The issue here is

If you know that at least one message from Alice goes through, and Alice says "do this with priority 0", then yes, you can solve the problem. The issue here is different to what you are modelling; imagine this payoff table for A B attacks B holds A attacks +1 -∞ A holds 0 0 The question is, knowing nothing about the reliability of the connection, is possible to have a strategy that has a positive expectation? B is only going to attack if they are absolutely certain you will, and vice-versa. The issue with your strategy is that even if Eve never interfered with the connection once, Alice does not know that, so will hold.