A perpetual search for talents across overlapping generations: A learning process

•We consider a class of multi-armed bandit problem (talents selection).•This class is arm-acquiring, restless and mortal bandit.•There is in general no index characterization.•We propose an optimal rule to select talents.•Our rule can be applied to multiple plays.

We consider a class of multi-armed bandit problems which is at the same time an arm-acquiring, restless and mortal bandit, and where the rewards follow any distribution. This is the case for a committee whose mission is to select the best element of a set of talents who live for KK periods, and who have different seniorities. In each period, new young talents enter the set. We find that if KK is infinite the problem is indexable. However, the index we find is different from that of Gittins, and is easier to be implemented. If KK is finite the problem is not indexable. In that case, we solve partially the problem. Under some condition, we develop a criterion to compare two talents. We also find that the solution we propose is still optimal in case of multiple plays.