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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)453-459
Number of pages7
JournalGames and Economic Behavior
Volume126
DOIs
StatePublished - Mar 2021

Keywords

  • Adaptive dynamics
  • Nash equilibria
  • Sequences of iterations
  • Tarski's theorem

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

Fingerprint

Dive into the research topics of 'On sequences of iterations of increasing and continuous mappings on complete lattices'. Together they form a unique fingerprint.

Cite this