Local Versions of Tarski’s Theorem for Correspondences

Abstract

For a strong set order increasing (resp., strongly monotone) upper order hemicontinuous correspondence mapping a complete lattice A into itself (resp., a σ-complete lattice into itself), we provide conditions for tight fixed-point bounds for sufficiently large iterations starting from any initial point in A. Our results prove a local version of the Veinott-Zhou generalization of Tarski’s theorem, as well as provide a new global version of the Tarski-Kantorovich principle for correspondences

Keywords: monotone iterations on correspondences, Tarski’s fixed-point theorem, Veinott-Zhou version of Tarski’s theorem for correspondences, Tarski-Kantorovich principle for correspondences, adaptive learning

JEL Classification: C62, C65, C72