When is there state independence?


Journal of Economic Theory

mai 2009, vol. 144, n°3, pp.1119-1134

Départements : Economie et Sciences de la décision, GREGHEC (CNRS)

Whether a preference relation can be represented using state-independent utilities as opposed to statedependent utilities may depend on which acts count as constant acts. This observation underlies an extension of Savage's expected utility theory to the state-dependent case that was proposed in this journal by Edi Karni. His result contains a condition requiring the existence of a set of acts which can play the role of constant acts and support a representation involving a state-independent utility function. This paper contains necessary and sufficient conditions on the preference relation for such a set of acts to exist. Results are obtained both for the Savage and the Anscombe and Aumann frameworks. Among the corollaries are representation theorems for state-dependent utilities. Relationships to Karni's work and extensions of the results are discussed.Keywords: Subjective expected utility; State-dependent utility; Monotonicity axiom