Multiple Exchange Property for M^♮-Concave Functions and Valuated Matroids

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 condition of Gul and Stacchetti is, in fact, equivalent to the gross substitutes condition of Kelso and Crawford.