This note considers a standard multinomial choice model. It is shown that if the distribution of additive utility shocks has a density, then the mapping from de- terministic components of utilities to choice probabilities is surjective. In other words, any vector of choice probabilities can be...

This paper explores the properties of expected value functions in dynamic discrete choice models. The continuity with respect to state variables and parameters, and the differentiability with respect to state variables are established under fairly general conditions. The differentiability with...