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Weak Monotone Comparative Statics

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  • Yeon-Koo Che
  • Jinwoo Kim
  • Fuhito Kojima

Abstract

We develop a theory of monotone comparative statics based on weak set order -- in short, weak monotone comparative statics -- and identify the enabling conditions in the context of individual choices, Pareto optimal choices% for a coalition of agents, Nash equilibria of games, and matching theory. Compared with the existing theory based on strong set order, the conditions for weak monotone comparative statics are weaker, sometimes considerably, in terms of the structure of the choice environments and underlying preferences of agents. We apply the theory to establish existence and monotone comparative statics of Nash equilibria in games with strategic complementarities and of stable many-to-one matchings in two-sided matching problems, allowing for general preferences that accommodate indifferences and incompleteness.

Suggested Citation

  • Yeon-Koo Che & Jinwoo Kim & Fuhito Kojima, 2019. "Weak Monotone Comparative Statics," Papers 1911.06442, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:1911.06442
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    References listed on IDEAS

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    1. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
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    5. Yuichiro Kamada & Fuhito Kojima, 2015. "Efficient Matching under Distributional Constraints: Theory and Applications," American Economic Review, American Economic Association, vol. 105(1), pages 67-99, January.
    6. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    7. Milgrom, Paul & Roberts, John, 1990. "Rationalizability, Learning, and Equilibrium in Games with Strategic Complementarities," Econometrica, Econometric Society, vol. 58(6), pages 1255-1277, November.
    8. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
    9. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    10. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
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    3. Tarun Sabarwal, 2023. "General theory of equilibrium in models with complementarities," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202307, University of Kansas, Department of Economics, revised Sep 2023.
    4. Minoru Kitahara & Yasunori Okumura, 2023. "School Choice with Multiple Priorities," Papers 2308.04780, arXiv.org, revised Oct 2024.
    5. Aniruddha Ghosh, 2024. "Robust Comparative Statics with Misspecified Bayesian Learning," Papers 2407.17037, arXiv.org.

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