Multi-agent cooperation problems are becoming more and more attractive in both civilian and military applications. In multi-agent cooperation problems, different network topologies will decide different manners of cooperation between agents. A centralized system will directly control the operation of each agent with information flow from a single centre, while in a distributed system, agents operate separately under certain communication protocols. In this paper, a systematic distributed optimization approach will be established based on a learning game algorithm. The convergence of the algorithm will be proven under the game theory framework. Two typical consensus problems will be analyzed with the proposed algorithm. The contributions of this work are threefold. First, the designed algorithm inherits the properties in learning game theory for problem simplification and proof of convergence. Second, the behaviour of learning endows the algorithm with robustness and autonomy. Third, with the proposed algorithm, the consensus problems will be analyzed from a novel perspective.