Trees and decisions

Carlos Alós-Ferrer and Klaus Ritzberger

Economic Theory, 2005, vol. 25, issue 4, 763-798

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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Keywords: Extensive form games; Sequential decisions; Trees. (search for similar items in EconPapers)
Date: 2005
References: Add references at CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00199-004-0487-3 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: Trees and Decisions (2003)
Working Paper: Trees and Decisions (2002)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joecth:v:25:y:2005:i:4:p:763-798

Ordering information: This journal article can be ordered from
http://www.springer. ... eory/journal/199/PS2

DOI: 10.1007/s00199-004-0487-3

Access Statistics for this article

Economic Theory is currently edited by Nichoals Yanneils

More articles in Economic Theory from Springer, Society for the Advancement of Economic Theory (SAET) Contact information at EDIRC.
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().