e*g
发帖数: 4981 | 1 Suppose there are two possible states H and L, with prior probability p and
1-p respectively. There are infinite rounds with a discount factor d. In
round 1, you could choose a value t_1 between 0 and constant a (a<1), If the
true state is H, you get H(t_1), otherwise you get L(t_1). H is increasing
in t, while L is decreasing in t. However, if you choose t_1, there is
probability of t_1 that you are informed the true state is L, if the true
state is L. Next in round 2, if you are informed, you know the state is L
and choose t_i=0 forever. If you are not informed, you bayesian update the
prior prob and choose t_2 again, and so on.
How to maximize your expectation?
The original question is a distance problem (H and L make an interval, and
you choose a point in between). I just generalize it a bit. Any kind of
input is appreciated!
Thanks!! |
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