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arXiv · 1911.06442

Monotone Comparative Statics without Lattices

Yeon-Koo Che·Jinwoo Kim·Fuhito Kojima
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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.

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Yeon-Koo Che, Jinwoo Kim, Fuhito Kojima. 2019-11-15. Monotone Comparative Statics without Lattices. https://arxiv.org/abs/1911.06442

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