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Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions

Huntley, Nathan; Troffaes, Matthias C.M.

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Authors

Nathan Huntley



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 Mar 29, 2024
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

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Copyright Statement
The original publication is available at www.springerlink.com




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