"Rationalizing Mindsets. A Bandit Model of Two-Dimensional Uncertainty"
Abstract: An agent is faced with a task and she is uncertain whether success can be achieved through effort or if it is only her natural ability that counts. Since in addition she does not know her own ability level, she is confronted with two-dimensional uncertainty. In each period, after deciding whether to exert effort or not, the agent observes a success or a failure and updates her beliefs about both the task and her ability accordingly. The agent gains information even when she is not exerting effort, therefore the task can be understood as a restless bandit. We characterize the agent's optimal strategy and show that different agents react to failure in different ways: while some agents find it optimal to resign, others prefer to increase their effort. Moreover, the optimal strategy may include repeated starting and stopping of exerting effort.