Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions

Huntley, Nathan; Troffaes, Matthias C.M.

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.

Citation

Huntley, N., & Troffaes, M. C. (2012). Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions. Annals of Operations Research, 195(1), 111-134. https://doi.org/10.1007/s10479-011-0968-2

• Journal Article Type: Article
• Publication Date: Jan 1, 2012
• Deposit Date: Feb 21, 2011
• Publicly Available Date: Apr 5, 2012
• Journal: Annals of Operations Research
• Print ISSN: 0254-5330
• Electronic ISSN: 1572-9338
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 195
• Issue: 1
• Pages: 111-134
• DOI: https://doi.org/10.1007/s10479-011-0968-2
• Public URL: https://durham-repository.worktribe.com/output/1510728