Iterative Monotone Comparative Statics

Abstract

For an increasing upper order hemi-continuous correspondence F selfmapping sigma-complete lattice A, we first provide tight fixed-point bounds for sufficiently large iterations on F starting from any initial point a in A. We use this result for conducting iterative fixed-point comparative statics, and then apply our results to monotone games and economies. For games of strategic complementarities, we improve the correspondence principle based results of Echenique (2002) by allowing for divergent learning processes, unstable fixed points, equilibrium indeterminacies, and unordered perturbations. We also apply our results to the comparative statics of stationary equilibria in large economies and the set of recursive equilibria in macroeconomic models with indeterminacies.