Low-Rank Graphon Estimation: Theory and Applications to Graphon Games

This paper tackles the challenge of estimating a low-rank graphon from sampled network data, employing a singular value thresholding (SVT) estimator to create a piecewise-constant graphon based on the network's adjacency matrix. Under certain assumptions about the graphon's structural properties, we establish bounds on the operator norm distance between the true graphon and its estimator, as well as on the rank of the estimated graphon. In the second part of the paper, we apply our estimator to graphon games. We derive bounds on the suboptimality of interventions in the social welfare problem in graphon games when the intervention is based on the estimated graphon. These bounds are expressed in terms of the operator norm of the difference between the true and estimated graphons. We also emphasize the computational benefits of using the low-rank estimated graphon to solve these problems.