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 distingueshed node, called the root. But an abstract graph is not a domain for decision theory. Decision theory perceives of acts as function 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.
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Paper provided by University of Vienna, Department of Economics in its series Vienna Economics Papers with number
0304.
Find related papers by JEL classification: C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
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