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<p>For an ascending correspondence <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F:X\rightarrow 2^X\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <msup> <mn>2</mn> <mi>X</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with chain-complete values on a complete lattice <i>X</i>, we prove that the set of fixed points is a complete lattice. This generalizes Zhou’s fixed point theorem. We provide an application to games with strategic complementarities.</p>

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Fixed point theorems for increasing correspondences on lattices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月5日

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  • Lu YU

摘要

For an ascending correspondence \(F:X\rightarrow 2^X\) F : X → 2 X with chain-complete values on a complete lattice X, we prove that the set of fixed points is a complete lattice. This generalizes Zhou’s fixed point theorem. We provide an application to games with strategic complementarities.