On sequences of iterations of increasing and continuous mappings on complete lattices

• 成果类型: Article
• 署名作者: Olszewski, Wojciech
• 署名单位: Northwestern University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.01.011
• 发表日期: 2021
• 页码: 453-459
• 关键词: Tarski's theorem; Sequences of iterations; Nash equilibria; Adaptive dynamics

摘要

We generalize the famous Tarski result by showing that: if Xis a complete lattice, and f: X -> X is an increasing and continuous mapping, then for all points x(0) is an element of X, the limits of sequences (f(n)(lim sup(k) f(k)(x(0))))(n=1)(infinity) and (f(n)(lim inf(k) f(k)(x(0))))(n=1)(infinity) are fixed points of f. These limits are the tight fixed-point bounds between which sufficiently large iterations f(k)(x(0)) are located. We provide an application of this result to studying best-response dynamics. (C) 2021 Elsevier Inc. All rights reserved.