Choosing on Sequences

The standard economic model of choice assumes that a decision maker chooses from sets of alternatives. A new branch of literature has considered the problem of choosing from lists i.e. ordered sets. In this paper, we propose a new framework that considers choice from infinite sequences. Our framework provides a natural way to model decision making in settings where choice relies on a string of recommendations. We introduce three broad classes of choice rules in this framework. Our main result shows that bounded attention is due to the continuity of the choice functions with respect to a natural topology. We introduce some natural choice rules in this framework and provide their axiomatic characterizations. Finally, we introduce the notion of computability of a choice function using Turing machines and show that computable choice rules can be implemented by a finite automaton.