Trees and Decisions

Carlos Alós-Ferrer and Klaus Ritzberger

Vienna Economics Papers from University of Vienna, Department of Economics

Abstract: The traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts define 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 function 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 definition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be defined as specific 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.

JEL-codes: C72 D70 (search for similar items in EconPapers)
Date: 2002-12
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Related works:
Journal Article: Trees and decisions (2005)
Working Paper: Trees and Decisions (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:vie:viennp:vie0304

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