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

Lu Yu

Papers from arXiv.org

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.

Date: 2024-07
New Economics Papers: this item is included in nep-gth
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