The standard model of decision analysis is modified by showing that, in general, the 'state of nature' concept can be usefully represented in terms of three components that may be called: (1) payoff relevant (2) payoff generating and (3) message generating. This modification allows a richer structure within which decision analysis problems can be formulated and thus allows a richer foundation for developing new concepts, classifying problems and revising existing concepts such as perfect iv.formation. It is shown that the unique payoff relevant domain of states and acts must, in any real decision, provide the initial basis for defining any payoff function (or, as appropriate, the loss function and opportunity loss function) that has a domain other than payoff-relevant states. This paper will modify the standard model of decision analysis by regarding the so-called state of nature as a triple: its first component is 'payoff relevant'; its second component is 'payoff generating'; and its third component is 'message generating'. To develop this, we wilt begin with a formulation of the basic decision analysis model and then use a simplified urn model to illustrate the three components. This will provide a reference for a more detailed development of the concept.
I. BASIC DECISION ANALYSIS MODEL
This basic model considers a decision maker (DM) who makes choices by maximizing his expected utility in accordance with the yon Neumann-Morgensternutility hypothesis [16]. The DM is uncertain about the relationship between his feasible actions -elements a of a set A -and the relevant outcome in the future. We will use z to index this uncertainty, where Z~ (z}. Then, assuming z finite for simplicity and denoting by p(z) the probability density over Z, we are able to define a utility function on A x Z, which we denote by u(a; z).
Thus for a given z the probability that action a yields utility u(a; z) is p(z). The DM then has the following maximization problem:
(1) Maxa~a~ z u(a; z)p(z).