Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids
Combinatorics
2017-04-12 v2
Abstract
The multiple exchange property for matroid bases is generalized for valuated matroids and M-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.
Cite
@article{arxiv.1608.07021,
title = {Multiple Exchange Property for M$^\natural$-concave Functions and Valuated Matroids},
author = {Kazuo Murota},
journal= {arXiv preprint arXiv:1608.07021},
year = {2017}
}
Comments
10 pages