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- Title
Trees and decisions.
- Authors
Alós-Ferrer, Carlos; Ritzberger, Klaus
- 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 making; DECISION theory; TREES; DEFINITIONS; GAMES
- Publication
Economic Theory, 2005, Vol 25, Issue 4, p763
- ISSN
0938-2259
- Publication type
Article
- DOI
10.1007/s00199-004-0487-3