Bounded memory in a changing world: Biases in behaviour and belief

A decision-maker faces a decision problem to choose an action, at a randomly determined time, to match an unknown state of nature. She has access to a sequence of signals partially informative of the current state of nature. The state of nature evolves according to a Markov chain. The decision-maker is subject to constraints on information-processing capacity, modelled here by a finite set of memory states. We characterize when optimal inference is possible with these constraints and, when it is not, what the optimal constrained inference is in two broad classes of environments. In the first class where the signals have similar strengths, optimal inference can be represented by simple rules corresponding to heuristics, like the “recency bias”, which have been studied by experimental researchers. In the second class where one signal is very informative, the constrained optimal rule ignores the possibility of regime changes.