Nash equilibria of games with generalized complementarities

TL;DR

This paper generalizes the concept of complementarities in games by introducing weaker conditions than existing ones, proving that Nash equilibria form a complete lattice under these conditions, extending Zhou's theorem.

Contribution

It introduces weaker conditions than quasisupermodularity and single crossing, and proves the lattice structure of Nash equilibria under these new conditions.

Findings

Nash equilibria form a nonempty complete lattice.

The conditions are weaker than quasisupermodularity.

The result generalizes Zhou's theorem.

Abstract

To generalize complementarities for games, we introduce some conditions weaker than quasisupermodularity and the single crossing property. We prove that the Nash equilibria of a game satisfying these conditions form a nonempty complete lattice. This is a purely order-theoretic generalization of Zhou's theorem.