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arXiv · 2407.18582

Order-theoretical fixed point theorems for correspondences and application in game theory

Lu Yu
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Abstract

For an ascending correspondence $F:X\to 2^X$ with chain-complete values on a complete lattice $X$, we prove that the set of fixed points is a complete lattice. This strengthens Zhou's fixed point theorem. For chain-complete posets that are not necessarily lattices, we generalize the Abian-Brown and the Markowsky fixed point theorems from single-valued maps to multivalued correspondences. We provide an application in game theory.

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Lu Yu. 2024-07-26. Order-theoretical fixed point theorems for correspondences and application in game theory. https://arxiv.org/abs/2407.18582

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