This paper introduces a multi-objective optimization based on a game theory technique for sizing and cost minimization of a grid-connected multi-microgrids. The multi-microgrid system comprised of three microgrids with various combinations of wind turbines, photovoltaic panels, and storage batteries to meet the load requirement. Due to the variability of generation resources, and to maintain lower energy cost, the benchmarks considered for multi-objective optimization are reliability and levelised cost of energy. The architecture is designed based on a Nash equilibrium game theory technique in which the generation resources and storage batteries are selected as three players. The simulation model is built in MATLAB software and particle swarm optimization algorithm is used for the optimization of the multi-microgrids. The benchmarks of multi-objective function are minimized to get suitable sizes of the players in a way that the optimum payoff values for the system is achieved. The feasibility of the game theoretic model is tested based upon the real time residential load, and weather data from three town of Australia.