A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis

TL;DR

This paper introduces a variational inequality framework to analyze Nash equilibria in network games, establishing conditions for existence, uniqueness, convergence, and sensitivity based on network properties.

Contribution

It provides a unified approach linking network spectral properties to equilibrium characteristics in complex network games.

Findings

Conditions on network matrices guarantee equilibrium existence and uniqueness.

Spectral norms and eigenvalues characterize convergence and stability.

Classes of networks satisfying these conditions are identified.

Abstract

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions.