Monotone Comparative Statics without Lattices
Theoretical Economics
2026-03-06 v5 Computer Science and Game Theory
Abstract
The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multidimensional environments such as mixed-strategy games where this property fails. We show that this structure is not essential. We introduce a weaker notion, the pseudo-lattice property, and preserve the theory's core results by generalizing the MCS theorems for individual choice and Tarski's fixed-point theorem. Our framework expands comparative statics to pseudo quasi-supermodular games. Crucially, it enables the first MCS analysis of mixed-strategy Nash equilibria and trembling-hand perfect equilibria.
Keywords
Cite
@article{arxiv.1911.06442,
title = {Monotone Comparative Statics without Lattices},
author = {Yeon-Koo Che and Jinwoo Kim and Fuhito Kojima},
journal= {arXiv preprint arXiv:1911.06442},
year = {2026}
}