We characterize two sorts of stochastic choice rules in which the agent makes current decisions using a forward-looking value function that takes future randomizations into account. Both sorts of rules generalize logistic choice, and are equivalent to it in static problems. The rules differ in...

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback-Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman (1990)'s...

We study learning and information acquisition by a Bayesian agent whose prior belief is misspecified in the sense that it assigns probability 0 to the true state of the world. At each instant, the agent takes an action and observes the corresponding payoff, which is the sum of a fixed but...

We study learning and information acquisition by a Bayesian agent who is misspecified in the sense that his prior belief assigns probability zero to the true state of the world. In our model, at each instant the agent takes an action and observes the corresponding payoff, which is the sum of the...

We show that the probability that Bayesian posteriors assign to the outcome distributions that do not ``best fit'' the empirical distribution in terms of Kullback-Leibler divergence converges to zero at a uniform and exponential rate, even when the prior does not have full support. This extends...

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback–Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990)...