Optimal Strategies for a Class of Constrained Sequential Problems

Abstract

This paper considers and unifies two sequential problems which have been extensively discussed. A class of sequential problems is proposed that includes both. An arbitrary partial ordering constraint is permitted to restrict possible strategies. An algorithm is proposed for finding the optimal strategy, and we prove that a strategy is optimal for the class of problems if and only if it can be found by the algorithm. The main tool is a set of functional equations in strategy space.