This paper addresses the robust optimal filtering design over unreliable networks, where the data packet dropouts occur during the signal transmission from the sensor side to the filter. The designed filter is expected, under communication data loss, to provide a guaranteed robustness against disturbance/model uncertainty while achieving the minimized variance of the estimation error under Gaussian white noises and the worst case of the disturbance. The Nash game approach is adopted to deal with such a multiobjective filtering problem. Based on the concept of the mean-square stability, Nash equilibrium strategies are analytically applied in terms of two cross-coupled modified algebraic Riccati equations. The presented design method provides a systematic way to achieve a tradeoff of the estimation performance in the $\mathcal {H}_2$ and $\mathcal {H}_\infty$ senses in the presence of data loss.