Welfare bounds for linear-quadratic network games
研究了线性二次网络博弈中纳什均衡的效率，发现福利比率（均衡福利与社会最优之比）的上下界完全由网络邻接矩阵的谱决定，下界由最大特征值确定，上界在矩阵秩亏时达到1，实证社会网络的上界接近1。
This paper quantifies the efficiency of the Nash equilibrium in the class of linear-quadratic network games. We show that the theoretical bounds of the welfare ratio, defined as the equilibrium welfare relative to the social optimum, are fully characterized by the spectrum of the adjacency matrix of the underlying network. Specifically, the lower bound of the welfare ratio is determined by the largest eigenvalue of the adjacency matrix, while the upper bound reaches unity whenever the matrix is rank-deficient. Applying the theory to empirical social networks, we find that the upper bounds tend to be close to unity.