Trees and Decisions

Carlos Alós-Ferrer and Klaus Ritzberger

No 129, Economics Series from Institute for Advanced Studies

Abstract: The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts de?ne a tree as a connected directed graph without loops and a distinguished node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as functions from states to consequences. Sequential decisions, accordingly, get conceptualized by mappings from sets of states to sets of consequences. Thus, the question arises whether a natural de?nition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be de?ned as speci?c collections of sets. Without loss of generality the elements of these sets can be interpreted as representing plays. Therefore, the elements can serve as states and consequences at the same time.

Keywords: Decision under uncertainty; Extensive form games; Trees (search for similar items in EconPapers)
JEL-codes: C72 D70 (search for similar items in EconPapers)
Pages: 40 pages
Date: 2003-03
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https://irihs.ihs.ac.at/id/eprint/2647 First version, 2003 (application/pdf)

Related works:
Journal Article: Trees and decisions (2005)
Working Paper: Trees and Decisions (2002)
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