Fixed Point Theorems for Correspondences With Values in a Partially Ordered Set and Extended Supermodular Games

Abstract

We present fixed point theorems for correspondences with values in a partially ordered set. generalizing Knaster-Tarski's fixed point theorem. We prove the existence of a Nash equilibrium for extended supermodular games. non-cooperative games where the strategy space is a quasi-lattice and the best reply satisfies certain monotonicity re-quirements.