Trees and Decisions
AbstractThe traditional model of sequential decision making, for instance, in extensive form games, is a tree. Most texts de?ne 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 de?nition of a tree can be given, where nodes are sets of states. We show that, indeed, trees can be de?ned as speci?c 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.
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Bibliographic InfoPaper provided by Institute for Advanced Studies in its series Economics Series with number 129.
Length: 40 pages
Date of creation: Mar 2003
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Other versions of this item:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
- D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
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- Joseph Greenberg & Sudheer Gupta & Xiao Luo, 2009. "Mutually acceptable courses of action," Economic Theory, Springer, vol. 40(1), pages 91-112, July.
- Alós-Ferrer, Carlos & Ritzberger, Klaus, 2008.
"Trees and extensive forms,"
Journal of Economic Theory,
Elsevier, vol. 143(1), pages 216-250, November.
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