I nerd-sniped myself last night with this question:
Two players alternate secretly choosing attack or defend. (Player 1 chooses first, then player 2 chooses, and so on). If you choose attack twice in a row, you win. But if you choose attack and your opponent chose attack last turn, you win immediately. Does this game have a Nash equilibrium, and if so, what is it? (or if there are multiple, find all of them)