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

• Tác giả: Lu Yu
• Ngôn ngữ: eng
• Ký hiệu phân loại: 519.3 Game theory
• Thông tin xuất bản: 2024
• Bộ sưu tập: Metadata
• ID: 203520

Tóm tắt

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.