Decisions over Sequences
This provides theoretical foundations for sequential decision-making models, relevant to economics and computer science.
The paper introduces decision rules for modeling sequential decision-making and establishes equivalence between stopping and uniform stopping rules, while showing that computable rules can be implemented with finite automata and that continuity implies computability for choice rules.
This paper introduces a class of objects called decision rules that map infinite sequences of alternatives to a decision space. These objects can be used to model situations where a decision maker encounters alternatives in a sequence such as receiving recommendations. Within the class of decision rules, we study natural subclasses: stopping and uniform stopping rules. Our main result establishes the equivalence of these two subclasses of decision rules. Next, we introduce the notion of computability of decision rules using Turing machines and show that computable rules can be implemented using a simpler computational device: a finite automaton. We further show that computability of choice rules -- an important subclass of decision rules -- is implied by their continuity with respect to a natural topology. Finally, we introduce some natural heuristics in this framework and provide their behavioral characterization.