Designing optimal interdependent networks is important for the robustness and efficiency of national critical infrastructures. Here, we establish a two-person game-theoretic model in which two network designers choose to maximize the global connectivity independently. This framework enables decentralized network design by using iterative algorithms. After a finite number of steps, the algorithm will converge to a Nash equilibrium, and yields the equilibrium topology of the network. We corroborate our results by using numerical experiments, and compare the Nash equilibrium solutions with their team solution counterparts. The experimental results of the game method and the team method provide design guidelines to increase the efficiency of the interdependent network formation games. Moreover, the proposed game framework can be generally applied to a diverse number of applications, including power system networks and international air transportation networks.