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(limsupkfk(x0)))n=1∞ and (fn(liminfkfk(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 language | English (US) |
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Pages (from-to) | 453-459 |
Number of pages | 7 |
Journal | Games and Economic Behavior |
Volume | 126 |
DOIs | |
State | Published - Mar 2021 |
Keywords
- Adaptive dynamics
- Nash equilibria
- Sequences of iterations
- Tarski's theorem
ASJC Scopus subject areas
- Finance
- Economics and Econometrics