In this paper, we propose a distributed solution based on game-theoretic approaches to the topology formation problem for mobile wireless sensor networks with multi-source multicast flows. Our solution significantly reduces computational complexity by taking advantage of network coding. Finding an optimal topology for network coding in multi-source multicast flows is NP-hard problem, so the proposed algorithm provides a suboptimal solution with low computational complexity. We formulate the problem of distributed network topology formation as a network formation game by considering the nodes in the network as players that can take actions for making outgoing links. The proposed game, which consists of multiple players and multicast flows, can be decomposed into independent link formation games played by only two players with a unicast flow. The proposed algorithm is also guaranteed to converge, i.e., a stable network topology can be always formed. Our simulation results confirm that the computational complexity of the proposed solution is low enough for practical deployment in large-scale mobile, wireless sensor networks.