Equivalent decision trees and their associated strategy sets
type: Item
instance of: scholarly article
title: Equivalent decision trees and their associated strategy sets
zbMATH Open document ID: 0614.90002
DOI: 10.1007/BF00127336
author: Irving H. La Valle
author: Peter Fishburn
published in: Theory and Decision
publication date: 1987-01-01T00:00:00Z
review text: The purpose of this paper is to examine the structure of individual decisions under uncertainty in extensive (i.e., decision-tree) form at a sufficient level of generality to encompass many traditional as well as novel criteria of general choice under uncertainty. Considerations both of structure and of strategic effect arise. In {\S} 2 we define weak and strong forms of strategic equivalence of decision trees and describe partial-normalization procedures by which all economically defined complete pure strategies may be identified for the decider and for ''chance''. In {\S} 3 we examine characteristics of locally randomized, ''behavior'' strategies for the decider as the degree of normalization is varied, and we deduce useful properties of the function which specifies an outcome lottery for each behavior strategy of the decider in conjunction with a deterministic or stochastic selection by Chance. In {\S} 4 we list a wide variety of choice criteria which may be invoked within the framework developed here.
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 3995380
zbMATH Keywords: individual decisions under uncertainty
zbMATH Keywords: strategic equivalence of decision trees
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3995380