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

2024/07/26 by Lu Yu, Yu, Lu
Computer Science · Engineering · Mathematics · #FOS: Economics and business #Fixed Point Theorems Analysis #Guidance and Control Systems #Optimization and Variational Analysis #Theoretical Economics (econ.TH)

paper · pdf · doi:10.48550/arxiv.2407.18582

openalex publication_date 2024/07/26 · openalex created_date 2024/09/30 · openalex updated_date 2026/07/28

Abstract

For an ascending correspondence 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 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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