When is there state independence?

Brian Hill (1)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC

Whether a preference relation can be represented using state-independent utilities as opposed to state-dependent 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

Domains: Economy and decision science

Brian Hill. When is there state independence?. Journal of Economic Theory, 2009, Vol.144,n°3, pp.1119-1134. ⟨10.1016/j.jet.2008.11.008⟩. ⟨hal-00463429⟩