Network Design for Social Welfare

TL;DR

This paper investigates how to design network structures in network games to align Nash equilibria with social optima, providing conditions on adjacency matrices for linear quadratic games and analyzing robustness and extensions.

Contribution

It introduces conditions on adjacency matrices to ensure Nash equilibria match social optima and explores solution uniqueness and robustness in networked games.

Findings

Conditions on adjacency matrices for social optimum alignment

Unique solution criteria via variational inequalities

Robustness of social cost under network perturbations

Abstract

In this paper, we consider the problem of network design on network games. We study the conditions on the adjacency matrix of the underlying network to design a game such that the Nash equilibrium coincides with the social optimum. We provide the examples for linear quadratic games that satisfy this condition. Furthermore, we identify conditions on properties of adjacency matrix that provide a unique solution using variational inequality formulation, and verify the robustness and continuity of the social cost under perturbations of the network. Finally we comment on individual rationality and extension of our results to large random networked games.