Most of us know the standard version of the Monty Hall “paradox”. If not: Monty Hall, a game show host invites a candidate to choose among three doors (A,B & C), one of of which hides a prize whereas the other two would reveal goats (which might also be perceived as a prize by some. I, however, doubt one would be allowed to actually take the goat.). The candidate chooses door A. Monty reveals a goat behind door B and offers the candidate to either stick to her choice or opt to switch to C. Bayesian updating tells us that it is optimal to switch in 2 out of 3 cases.
Credit to my friend Pantelis Loupos for the idea behind what is to follow: Suppose Monty has two candidates, for simplicity a man and a woman. Upon first request the man chooses A whereas the woman goes for C. Monty reveals that door B was covering a goat and asks both candidates whether they would like to stick to their initial choice or switch to the other candidate’s. Suppose that both would receive the prize if choosing the correct door. Does the Monty Hall “paradox” suggest that by switching doors candidates both increase their chance of winning?