Decision trees are useful graphical representations of sequential decision problems. We consider decision trees where events are assigned imprecise probabilities, and examine their normal form decisions; that is, scenarios in which the subject initially decides all his future choices. We present a backward induction method for efficiently finding the set of optimal normal form decisions under maximality. Our algorithm is similar to traditional backward induction for solving extensive forms in that we solve smaller subtrees first, however it is different in that solutions of subtrees are only used as intermediate steps to reach the full solution more efficiently—in particular, under maximality, a decision that is optimal in a subtree can be potentially absent in any optimal policy in the full tree.
展开▼
