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On Smithson's fixed point theorem for order preserving multifunctions

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  • Haruki Kono
  • Mark Voorneveld

Abstract

Fixed point theorems are ubiquitous in economic research. Many studies cite Smithson (1971) ``Fixed points of order preserving multifunctions,'' yet the original proof contains errors. This note presents a new, concise proof and explains why Smithson's argument is invalid. It also contains new results on the structure of the set of fixed points and monotone comparative statics.

Suggested Citation

  • Haruki Kono & Mark Voorneveld, 2023. "On Smithson's fixed point theorem for order preserving multifunctions," Papers 2303.15483, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2303.15483
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    References listed on IDEAS

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    1. Aniruddha Ghosh, 2024. "Robust Comparative Statics with Misspecified Bayesian Learning," Papers 2407.17037, arXiv.org, revised Mar 2025.
    2. Daron Acemoglu & Martin Kaae Jensen, 2015. "Robust Comparative Statics in Large Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 123(3), pages 587-640.
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