We show that the class of preferences satisfying the Gross Substitutes condition of Kelso and Crawford (1982) is strictly larger than the class of Endowed Assignment Valuations of Hatfield and Milgrom (2005), thus resolving the open question posed by the latter paper. In particular, our result...

A Bernoulli factory is an algorithmic procedure for exact sampling of certain random variables having only Bernoulli access to their parameters. Bernoulli access to a parameter p ∈ [0, 1] means the algorithm does not know p, but has sample access to independent draws of a Bernoulli random...