A Bandit Model of Two-Dimensional Uncertainty -- Rationalizing Mindsets

We analyze a new type of bandit where an agent is confronted with two-dimensional uncertainty. The agent does not know whether ability or effort is required to succeed at a given task. Moreover, the agent does not know her own ability level. 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. In contrast to a standard bandit model, the agent gains information even when she is not exerting effort. In this setting different agents react to failure in different ways; while some agents find it optimal to resign others prefer to increase their effort. We show that different effort costs and beliefs about the own ability and the production function together with Bayesian updating can explain the differences in behavior.