Rational Inattention with Sequential Information Sampling

We propose a new principle for measuring the cost of information structures in rational inattention problems, based on the cost of generating the information used to make a decision through a dynamic evidence accumulation process. We introduce a continuous-time model of sequential information sampling, and show that, in a broad class of cases, the choice frequencies resulting from optimal information accumulation are the same as those implied by a static rational inattention problem with a particular static information-cost function. Among the static cost functions that can be justified in this way is the mutual information cost function proposed by Sims [2010], but we show that other cost functions can be justified in this way as well. We introduce a class of "neighborhood-based" cost functions, which also summarize the results of dynamic evidence accumulation, and (unlike mutual information) incorporate a conception of the similarity of states to one another, making it more costly to undertake experiments that can produce different results in similar but non-identical states. With this alternative cost function, optimal information accumulation results in choice frequencies that are similar in similar states; in a continuous-state extension of the model, optimality implies choice frequencies that vary continuously with the state, even when the choice payoffs jump discontinuously with variation in the state. This feature of our version of the rational inattention model conforms with evidence from perceptual discrimination experiments.