Transient improvements in parallel connected inverter systems have become a vital part in the modern microgrid control arena. Owing to the low generation inertia and the spinning reserve, parallel connected inverters in the microgrid environment are highly vulnerable to transient instabilities. Decentralized transient trajectory optimization methodology for a parallel connected inverter system in an islanded microgrid is introduced in this paper. Non-cooperative differential game theoretic approach is developed to dynamic path optimization of the parallel connected inverters which are treated as the dynamic source players in the system. Optimum control signal trajectory generation and the dynamic modeling of the system is done in the d-q rotating reference frame. Example simulations were carried out based on a simple test system to illustrate the applicability and the effectiveness of the proposed approach.