Common knowledge (CK) human subject experiments on a simulated environment of the Facebook social media platform are of great interest to understand how agents (players) reason and coordinate actions based on information collected over a network. However, outcomes from CK experiments often deviate from the outcomes of the theoretical CK model. It is important to model and analyze such deviations. Due to the prohibitive cost of conducting CK experiments for every player under all combinations of experimental factors, each player typically participates in only a subset of experiments. In this work, we propose a covariate-augmented factorization approach (CAFA) to model discrepancies between CK experimental data and theoretical CK predictions. The proposed CAFA considers latent factors to factorize the discrepancy matrix with respect to players and CK experiments, augmented by experimental covariates as additional regressors. The numerical analysis on real experimental data shows that the proposed CAFA not only achieves high prediction accuracy but also provides insight on important experimental factors affecting the discrepancy.