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.

翻译：在本文中,我们考虑网络游戏的网络设计问题。我们研究基本网络的相邻矩阵的条件,以设计一种游戏,使纳什平衡与社会最佳平衡相吻合。我们为满足这一条件的线性二次游戏提供了范例。此外,我们确定对相邻矩阵特性的条件,这些条件提供了一种独特的解决办法,使用变式不平等公式,并核查网络干扰下社会成本的稳健性和连续性。最后,我们评论了个人合理性,并将我们的结果扩大到大型随机网络游戏。