The problem with this solution is that the doctors can precommit to always diagnosing ill through acausal trade, so that they are rewarded in the case that they are the one who is randomly chosen for treatment (assuming they know the game).
The problem with this solution is that the doctors can precommit to always diagnosing ill through acausal trade, so that they are rewarded in the case that they are the one who is randomly chosen for treatment (assuming they know the game).