By incorporating the reciprocity into the utility function, this paper develops a game model of team production, which descripts the ability and the reciprocity simultaneously, to probe the intrinsic mechanism by which the reciprocity influences the team efficiency under different game timing. It is found that the reciprocity may promote the Pareto improvement of the team efficiency, which is irrelative with the ability. As long as the final mover is a reciprocal instead of a standard self-interest one, the extent of Pareto improvement under sequential game is bigger than that under simultaneous game even if agents except the final reciprocal one move randomly. Therefore, the principal should select reciprocal agents to establish team and to ensure that the agents move sequentially. It offers a new theoretical explanation for the existence of the principal, and a new approach for team incentives.