In wireless sensor networks, achieving load balancing in an energy-efficient manner to improve the network lifetime as much as possible is still a challenging problem because in such networks, the only energy resource for sensor nodes is their battery supplies. This paper proposes a game theoretical-based solution in the form of a distributed algorithm for constructing load-balanced routing trees in wireless sensor networks. In our algorithm, load balancing is realized by adjusting the number of children among parents as much as possible, where child adjustment is considered as a game between the parents and child nodes; parents are considered as cooperative players, and children are considered as selfish players. The gained utility by each node is determined by means of some utility functions defined per role, which themselves determine the behavior of nodes in each role. When the game is over, each node gains the maximum benefit on the basis of its utility function, and the balanced tree is constructed. The proposed method provides additional benefits when in-network aggregation is applied. Analytical and simulation results are provided, demonstrating that our proposed algorithm outperform two recently proposed benchmarking algorithms [1,2], in terms of time complexity and communication overhead required for constructing the load-balanced routing trees.