  We present a two-armed bandit model of decision making under uncertainty
where the expected return to investing in the "risky arm" increases when
choosing that arm and decreases when choosing the "safe" arm. These dynamics
are natural in applications such as human capital development, job search, and
occupational choice. Using new insights from stochastic control, along with a
monotonicity condition on the payoff dynamics, we show that optimal strategies
in our model are stopping rules that can be characterized by an index which
formally coincides with Gittins' index. Our result implies the indexability of
a new class of restless bandit models.
