Equivalent decision trees and their associated strategy sets

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 § 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 § 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 conjuction with a deterministic or stochastic selection by Chance. In § 4 we list a wide variety of choice criteria which may be invoked within the framework developed here.