In this note we prove that the class of valuation functions representable via integral assignment messages is a proper subset of strong substitutes valuations. Thus, there are strong substitutes valuations not expressible via assignment messages.
Cite
@article{arxiv.2107.05051,
title = {On the Expressiveness of Assignment Messages},
author = {Maximilian Fichtl},
journal= {arXiv preprint arXiv:2107.05051},
year = {2021}
}