Existence and structure of Nash equilibria for supermodular games

TL;DR

This paper proves two theorems related to sublattice topology and applies them to extend classical results on the existence and structure of Nash equilibria in supermodular games, correcting previous proof errors.

Contribution

It provides new topological theorems for sublattices and extends classical results on Nash equilibria in supermodular games, with corrections to Zhou's proof.

Findings

Proved two theorems about sublattice topologies.

Extended classical results on Nash equilibria existence.

Corrected errors in Zhou's proof.

Abstract

Two theorems announced by Topkis about the topological description of sublattices are proved. They are applied to extend some classical results concerning the existence and the order structure of Nash equilibria of certain supermodular games, with some problems in Zhou's proof corrected.