We consider network games where a large number of agents interact according to a network sampled from a random network model, represented by a graphon. By exploiting previous results on convergence of such large network games to graphon games, we examine a procedure for estimating unknown payoff parameters, from observations of equilibrium actions, without the need for exact network information. We prove smoothness and local convexity of the optimization problem involved in computing the proposed estimator. Additionally, under a notion of graphon parameter identifiability, we show that the optimal estimator is globally unique. We present several examples of identifiable homogeneous and heterogeneous parameters in different classes of linear quadratic network games with numerical simulations to validate the proposed estimator.

翻译：我们考虑一类大规模网络博弈，其中大量智能体依据随机网络模型（由图极限表示）采样的网络进行交互。基于此前关于此类大规模网络博弈收敛至图极限博弈的研究结果，我们提出了一种方法：通过观测均衡行动来估计未知收益参数，且无需精确的网络信息。我们证明了该估计量求解所涉及的优化问题的光滑性和局部凸性。此外，在图极限参数可识别性概念下，我们证明了最优估计量具有全局唯一性。针对不同类别的线性二次型网络博弈，我们给出了若干可识别的同质与异质参数示例，并通过数值模拟验证了所提出的估计量。