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Monotone Comparative Statics without Lattices

Author

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  • Yeon-Koo Che
  • Jinwoo Kim
  • Fuhito Kojima

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.

Suggested Citation

  • Yeon-Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Monotone Comparative Statics without Lattices," Papers 1911.06442, arXiv.org, revised Mar 2026.
    • Handle: RePEc:arx:papers:1911.06442
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    References listed on IDEAS

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    Cited by:

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    2. Gregorio Curello & Ludvig Sinander, 2022. "The comparative statics of persuasion," Papers 2204.07474, arXiv.org, revised Nov 2025.
    3. Sabarwal, Tarun, 2025. "General theory of equilibrium in models with complementarities," Journal of Economic Theory, Elsevier, vol. 224(C).
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    5. Vives, Xavier & Vravosinos, Orestis, 2024. "Strategic complementarity in games," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    6. Aniruddha Ghosh, 2024. "Robust Comparative Statics with Misspecified Bayesian Learning," Papers 2407.17037, arXiv.org, revised Mar 2025.

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