A simple derivation of the Williams-Daly-Zachery theorem
2012 (English)Report (Other academic)
In this note we give a simple elementary proof of the Williams-Daly-Zachery theorem for additive random utility (ARU) models. This theorem says that the choice probabilities in an ARU model are the partial derivatives of the expected achieved utility. This is proved under the condition that the choice probabilities are continuous. We further prove that the choice probabilities are continuous exactly when the probability of ties is zero. Finally we prove that the probability of ties is zero if the cdf of the random term (of the ARU model) is differentiable with locally bounded gradient.
Place, publisher, year, edition, pages
Transport Systems and Logistics
IdentifiersURN: urn:nbn:se:kth:diva-95398OAI: oai:DiVA.org:kth-95398DiVA: diva2:528087
QC 201205242012-05-242012-05-242012-05-24Bibliographically approved