Stochastic choice with limited memory

We model a decision maker who observes available alternatives according to a list and stochastically forgets some alternatives. Each time the decision maker observes an item in the list, she recalls previous alternatives with some probability, conditional on those alternatives being recalled until this point. The decision maker maximizes a preference relation over the set of alternatives she can recall. We show that if every available alternative is chosen with strictly positive probability, the preference order and the list order must coincide in any limited memory representation. Under the full support assumption, the preference ordering, the list ordering and the memory parameters are uniquely identified up to the ranking of the two least preferred alternatives. We provide conditions on observable choice probabilities that characterize the model under the full support assumption. We then apply our model to study the pricing problem of a monopolist who faces consumers with limited memory. We show that when the probability of forgetting is high, the monopolist is better off charging a lower price than the optimal price in the perfect memory case.