What does this research mean for the field?

The set of fixed points of an ascending correspondence with chain-complete values on a complete lattice is itself a complete lattice. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The aim is to prove that the set of fixed points for ascending correspondences on complete lattices forms a complete lattice.

March 6, 2026Open Access

Fixed point theorems for increasing correspondences on lattices

LYLu YUUniversité Paris 1 Panthéon-Sorbonne

Key Points

The aim is to prove that the set of fixed points for ascending correspondences on complete lattices forms a complete lattice.
Utilized ascending correspondences defined from set X to its power set
Established conditions for chain-completeness on complete lattices
Generalized existing theorems to expand the understanding of fixed points
Proved that the fixed point set of ascending correspondences is indeed a complete lattice
Generalized Zhou's fixed point theorem for practical applications
Applied findings to analyze games with strategic complementarities

Abstract

Abstract For an ascending correspondence F: X 2X 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.

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