Generalization of Zhou fixed point theorem

TL;DR

This paper extends Zhou's fixed point theorem by weakening key conditions and applies these results to generalize Topkis's theorem on Nash equilibria in supermodular games.

Contribution

It introduces two new generalizations of Zhou's fixed point theorem, relaxing the subcompleteness and ascending conditions.

Findings

Generalized fixed point theorem under weaker conditions

Extended Topkis's theorem for Nash equilibria

Broader applicability in supermodular game analysis

Abstract

We give two generalizations of the Zhou fixed point theorem. They weaken the subcompleteness condition of values, and relax the ascending condition of the correspondence. As an application, we derive a generalization of Topkis's theorem on the existence and order structure of the set of Nash equilibria of supermodular games.