EXTENSIVE AND NORMAL FORM
P. J. Hammond opens his important 1988 paper by writing:
An almost unquestioned hypothesis of modern normative decision theory is that acts are valued by their consequences. Indeed, Savage (1954) defines an act as a function mapping uncertain states of the world into a domain of conceivable consequences, thus identifying an act with the state-contingent consequence function which it generates.(Hammond, 1988, p. 25)
Hammond thinks that much of the controversy concerning acceptable principles of rational behavior (such as, for example, the status of the requirement that preferences should be weakly ordered and should satisfy the independence postulate) could be resolved if we appreciated the implications of the “almost unquestioned” consequentialism lying at the core of modern normative decision theory for sequential decision making.
When an agent faces a choice among a set of available options, some or all of them may present him with fresh opportunities for choice among options which, in turn, may yield new opportunities for choice and so on. The decision problem is representable in a “tree form” or “extensive form” illustrated by Figure 4.1.
At stage 1, the agent has a pair of options A and B. Option A has as a sure consequence that the agent confronts a choice between 1 and 2. Option B has as a sure consequence that the agent confronts a choice between 3 and 4. In more sophisticated examples, the sequences of stages at which opportunities for choice arise can ramify.