Regarding the question of how to force all the incentives into one box, what about the following strategy: choose box 1 with probability 1 - (400 - x) epsilon, where x is the payoff of box 1. Then it is obviously in each host’s interest to predict box 1, since it has the largest probability of any box, but then it is also in each host’s interest to minimize 400 - x i.e. maximize x. This is true even though the hosts’ competition is zero-sum.

If the hosts are all predicting box 1, why does it matter with what probability the human picks box 1? (If the hosts’ payoffs for all-predict-correctly and all-predict-incorrectly are different, then their game isn’t zero-sum.)

I guess Austria is the AI because

it consistently capitalizes place names.