Normal form backward induction for decision trees with coherent lower previsions

TL;DR

This paper investigates the application of backward induction to decision trees under lower previsions, identifying when it is effective for certain choice functions and proposing approximation methods for others.

Contribution

It extends backward induction to decision trees with lower previsions, clarifies its applicability to various choice functions, and suggests approximation techniques for computational efficiency.

Findings

Backward induction works for maximality and E-admissibility.

It does not work for interval dominance and Gamma-maximin.

Approximate methods can still yield useful solutions.

Abstract

We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended backward induction to arbitrary choice functions, yielding far more efficient solutions, and we identified simple necessary and sufficient conditions for this to work. In this paper, we show that backward induction works for maximality and E-admissibility, but not for interval dominance and Gamma-maximin. We also show that, in some situations, a computationally cheap approximation of a choice function can be used, even if the approximation violates the conditions for backward induction; for instance, interval dominance with backward induction will yield at least all maximal normal form solutions.