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arXiv · 2303.15483

On Smithson's fixed point theorem for order preserving multifunctions

Haruki Kono·Mark Voorneveld
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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.

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Haruki Kono, Mark Voorneveld. 2026-02-17. On Smithson's fixed point theorem for order preserving multifunctions. https://arxiv.org/abs/2303.15483

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