  We study a novel family of behavioral policies for the multi-armed bandit
(MAB) problem, which we have termed Myopic Quantal Response (MQR). MQR
prescribes a simple way to randomize over arms according to historical rewards
and a "coefficient of exploitation," which explicitly manages the
exploration-exploitation trade-off. MQR is a dynamic adaptation of quantal
response models where the anticipated utilities are directly derived from past
rewards. Furthermore, it can be viewed as a generalization of the Thompson
Sampling (TS) algorithm. We develop an asymptotic theory for MQR and show how
it can help understand not only asymptotically optimal policies like TS, but
also those that are suboptimal due to "under" or "over" exploring. In the
non-asymptotic setup, we demonstrate how MQR can be used as a structural
estimation tool: Given observed data (i.e., realized actions and rewards), we
can estimate the implied coefficient of exploitation of any given policy
(either generated by human beings or algorithms). This allows us to diagnose
whether and to what extent the policy underexplores or overexplores.
