  The multiple exchange property for matroid bases is generalized for valuated
matroids and M$^\natural$-concave set functions. The proof is based on the
Fenchel-type duality theorem in discrete convex analysis. The present result
has an implication in economics: The strong no complementarities (SNC)
condition of Gul and Stacchetti is in fact equivalent to the gross substitutes
(GS) condition of Kelso and Crawford.
