Subjective Expected Utility Theory with Costly Actions - Economics ...

It seems, therefore, that an examination of the axiomatic foundations of subjective
expected utility theory for decision makers with direct preferences over
actions is warranted. As in other …elds, this study is intended to uncover and
allow clearer understanding of the behavioral premises underlying the theory,
thereby opening the way to a critical examination of its basic tenets.
In this paper I invoke the state-space formulation and pursue an approach in
which decision makers are supposed to have preference relations on M(A)£F jAj ;
where M (A) is the set of probability measure on A; and F is the subset of X S
containing all the simple acts: The resulting model …ts naturally situations in
which the eventual outcome is determined by the state of nature and stateindependent
actions taken by the decision maker, such as the decisions of the
agent in agency theory.
2 Preference Structures and Representations
2.1 Preliminaries
Let S be an in…nite set whose elements are states of nature and whose subsets
are events. Consequences, or outcomes, are real numbers representing monetary
payo¤s. Let the set of outcomes, X; be a compact interval in the real line.
Following Savage (1954), an act is a function from the set of states to the set
of outcomes. Let F denote the set of simple acts, namely, acts under which the
image of S is …nite. Assume that F is endowed with the product topology, then
it is a compact set. Denote by f a generic element of F and by x the constant
act f (s) =x for all s 2 S:
Let A = fa1; :::; ang; 2 · n