Trees and Decisions

Alós-Ferrer, Carlos and Ritzberger, Klaus (March 2003) Trees and Decisions. Former Series > Working Paper Series > IHS Economics Series 129


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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 isnot 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 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.;

Item Type: IHS Series
Keywords: 'Decision under uncertainty' 'Extensive form games' 'Trees'
Classification Codes (e.g. JEL): C72, D70
Date Deposited: 26 Sep 2014 10:37
Last Modified: 26 May 2024 06:02
ISBN: 1605-7996

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