Due to the increasing use of renewables into the grid connected through power converters, the rotational inertia in power systems has been reducing. Consequently the frequency response requires the activation of the so-called synthetic inertia control. The synthetic inertia control aims to inject an extra power component when the system experiences a frequency disturbance event. In this paper, it is proposed that a distributed dynamic controllers for sharing the synthetic inertia control actions between the various active power converters in the grid for the improvement of the frequency response. It is assumed that a communication structure between the synthetic inertia controllers and the local power converters is involved in the system. The convergence of the control system is reached through a game population theory and the primary frequency control has been improved. The results are validated based on simulation of a two-area test system.