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

Wojciech Olszewski

Games and Economic Behavior, 2021, vol. 126, issue C, 453-459

Abstract: We generalize the famous Tarski result by showing that: if X is a complete lattice, and f:X→X is an increasing and continuous mapping, then for all points x0∈X, the limits of sequences (fn(lim⁡supk⁡fk(x0)))n=1∞ and (fn(lim⁡infk⁡fk(x0)))n=1∞ are fixed points of f. These limits are the tight fixed-point bounds between which sufficiently large iterations fk(x0) are located. We provide an application of this result to studying best-response dynamics.

Keywords: Tarski's theorem; Sequences of iterations; Nash equilibria; Adaptive dynamics (search for similar items in EconPapers)
JEL-codes: C65 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:126:y:2021:i:c:p:453-459

DOI: 10.1016/j.geb.2021.01.011

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