Unless they expect that all other monks would think similarly, in which case they can take Priority without risk.
[Edit for my own memory: In game theoretic terms, they expect a large amount of utility if they decide to take Priority but others don’t, while they expect a rather larger amount of disutility if they decide to take Priority and others also do. In other words, they experience a utility gain only if they decide to take Priority using an algorithm different from the one used by the other monks. That seems to imply a “contrarian” decision theory, which decides based on the decision theory held by the other monks… but the existence of more than one contrarian would negate the benefit of being a contrarian at all… Needs more thought.]
The wise monks would avoid correctly guessing the traveler’s news (at least out loud), lest their lives depend upon repeating the performance.
Unless they expect that all other monks would think similarly, in which case they can take Priority without risk.
[Edit for my own memory: In game theoretic terms, they expect a large amount of utility if they decide to take Priority but others don’t, while they expect a rather larger amount of disutility if they decide to take Priority and others also do. In other words, they experience a utility gain only if they decide to take Priority using an algorithm different from the one used by the other monks. That seems to imply a “contrarian” decision theory, which decides based on the decision theory held by the other monks… but the existence of more than one contrarian would negate the benefit of being a contrarian at all… Needs more thought.]