2014/10/20 by Drapeau, Samuel, Jamneshan, Asgar
#91B06 #FOS: Economics and business #General Economics (econ.GN)
paper · doi:10.48550/arxiv.1410.5466
We provide an axiomatic system modeling conditional preference orders which is based on conditional set theory. Conditional numerical representations are introduced, and a conditional version of the theorems of Debreu on the existence of numerical representations is proved. The conditionally continuous representations follow from a conditional version of Debreu's Gap Lemma the proof of which relies on a conditional version of the axiom of choice, free of any measurable selection argument. We give a conditional version of the von Neumann and Morgenstern representation as well as automatic conditional continuity results, and illustrate them by examples.