Edit: Actually nevermind, this is just counterfactual mugging. Deleting post.

We have two superintelligent rational entities, call them alpha and omega, and they have access to each other's source code. They're playing one round of paper scissor rock. The winner gives the loser five dollars, or nothing if they tie. Additionally, you win $100 in bonus money from the bank if your opponent chooses scissors.

My question is, what would they do? If it was ordinary paper scissor rock, it seems fairly clear they can't do better than picking randomly, given that they're equally matched. But what do they do here? Is there in fact a right answer, or does it depend on the peculiarities of how they were programmed?