[UTMD-126] Monotone Comparative Statics without Lattices (by Yeon-Koo Che, Jinwoo Kim, Fuhito Kojima) (Revised version of UTMD-021)

Yeon-Koo Che, Jinwoo Kim, Fuhito Kojima

The theory of Monotone Comparative Statics (MCS) has traditionally required a lattice structure, excluding certain multi-dimensional environments like mixed-strategy games where this property fails. We show this structure is not essential. We introduce a weaker notion, 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.