Uncertainty and Probability Secretary Problem

Ambiguous Secretary Problem

Solution

the optimal stopping rule is simple

the payoff of simple ruleris recursively given by

φ(N) =aN

φ(r) =arBr+ (1−ar)φ(r+ 1)

explicit solution

φ(r) =

∑N

n=r

βn

n∏− 1

k=r

αk

for

βn= 1 −anb

n

,αn=^11 −−abn

n

r∗= inf{r≥1 :wr≤ 1 }forwr=

∑N

n=rβn

∏n− 1

k=rαkis uniquely

determined