Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/71246
Authors: 
Alós-Ferrer, Carlos
Ritzberger, Klaus
Year of Publication: 
2003
Series/Report no.: 
Reihe Ökonomie / Economics Series, Institut für Höhere Studien (IHS) 129
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 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.
Subjects: 
decision under uncertainty
extensive form games
trees
JEL: 
C72
D70
Document Type: 
Working Paper

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