A Tarski–Kantorovich theorem for correspondences

Łukasz Balbus, Wojciech Olszewski, Kevin Reffett and Łukasz Woźny

Journal of Mathematical Economics, 2025, vol. 118, issue C

Abstract: For a weakly monotone (resp., strongly monotone) upper order hemicontinuous correspondence F:A⇉A, where A is a complete lattice (resp., a σ-complete lattice), we provide tight fixed-point bounds for sufficiently large iterations Fk(a0), starting from any point a0∈A. Our results, hence, prove a generalization of the Tarski–Kantorovich theorem. We provide an application of our results to a class of social learning models on networks.

Keywords: Iterations of monotone correspondences; Tarski’s fixed-point theorem; Veinott–Zhou version of Tarski’s theorem for correspondences; Tarski–Kantorovich theorem for correspondences; Adaptive learning (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:118:y:2025:i:c:s0304406825000230

DOI: 10.1016/j.jmateco.2025.103106

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