A check for rational inattention

Models of rational inattention allow agents to make mistakes in their actions while assuming they do not make mistakes in attention allocation. I test this assumption by comparing attention’s marginal benefit (better actions) and marginal cost (less time for future decisions) using millions of online chess moves. I cannot reject that skilled players equalize marginal benefit and marginal cost across different time controls. Bad players, when they have little time, under-adjust their attention allocation, leading them to have higher marginal cost. A simple intervention improves players' attention allocation.