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...

For symmetric auctions, there is a close relationship between distributions of order statistics of bidders’ valuations and observable bids that is often used to estimate or bound the valuation distribution, optimal reserve price, and other quantities of interest nonparametrically. However, we...

Prediction markets for future events are increasingly common and they often trade several contracts for the same event. This paper considers the distribution of a normative risk-neutral trader who, given any portfolio of contracts traded on the event, would choose not to reallocate that...

We study a simultaneous, complete-information game played by p = 1 P agents. Each p has an ordinal decision variable Y p ∈ A p ={ 0 1 M p} , where M p can be unbounded, A p is p’s action space, and each element in A p is an action , that is, a potential value for Y p . The collective action...

Although survey‐based point predictions have been found to outperform successful forecasting models, corresponding variance forecasts are frequently diagnosed as heavily distorted. Professional forecasters who report inconspicuously low ex ante variances often produce squared forecast errors...