On Smithson's fixed point theorem for order preserving multifunctions
Combinatorics
2026-02-18 v4 Theoretical Economics
Abstract
Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains why Smithson's argument is invalid. It also contains new results on the structure of the set of fixed points and monotone comparative statics.
Cite
@article{arxiv.2303.15483,
title = {On Smithson's fixed point theorem for order preserving multifunctions},
author = {Haruki Kono and Mark Voorneveld},
journal= {arXiv preprint arXiv:2303.15483},
year = {2026}
}