Sorry to revive this topic... but I'm quite confused in the solution to part (2)
"select ... the action that, if Q discovered P were intending to take it, would lead Q to refuse to confess"
Everyone above says the answer is "Refuse to confess that Q stole"
That would mean the following statement is true:
If Q discovered that P were intending to [Refuse to confess that Q stole], then Q would refuse to confess
But if Q knows that P is going to refuse to confess, then Q's options are:
1) Refuse to confess -> Both P & Q refuse leads to both losing toy for 1 day
2) Confess -> Q Confesses, P refuses leads to Q getting toy immediately and P losing toy for 7 days
Since the problem specifies that "Both P and Q want only to maximize their own play time with their favorite toy," that means Q doesn't mind that P loses their toy for 7 days. Q only cares about minimizing their own punishment.
So if P refuses to confess, wouldn't Q's best path be to confess to get the toy immediately?
What am I missing in the above solution?
Similarly, if Q knows that P is going to confess, then Q's options are:
1) Refuse to confess -> Q loses toy for 7 days, P gets toy immediately
2) Confess -> Both confess, Q & P both lose toy for 3 days
In this situation, Q's best path is still to Confess, to minimize the number of days without their toy (3 days instead of 7 days)
I'm stuck, because in both cases it seems like Q's best path is always to Confess, but the problem asks for when will Q decide their best path is to refuse to confess