I’m assuming that race and sex and all other discernable features are independent and identically distributed, and also that the game overseer will not pay the doctors if they coordinate on obvious patterns involving race, sex, etc.
If only a few of the patients are ambiguously ill, it might be possible to discern this by observing an almost perfect agreement between ensemble diagnoses. In the iterated game, this might cause the doctors to preferentially flip diagnoses that they think are more ambiguous or not flip diagnoses that they think are more certain. This is not a perfect guarantee, of course.
They could coordinate based on patient race, or sex.
Whatsmore, if the line between ill and hale is at all ambiguous or hard to measure precisely, this method starts to fail hard.
I’m assuming that race and sex and all other discernable features are independent and identically distributed, and also that the game overseer will not pay the doctors if they coordinate on obvious patterns involving race, sex, etc.
Which now requires that the overseer knows these.
If only a few of the patients are ambiguously ill, it might be possible to discern this by observing an almost perfect agreement between ensemble diagnoses. In the iterated game, this might cause the doctors to preferentially flip diagnoses that they think are more ambiguous or not flip diagnoses that they think are more certain. This is not a perfect guarantee, of course.