Network selection is a key problem when a user faces multiple available wireless networks. Especially, this problem becomes more complicated when multiple users share multiple wireless networks due to the interaction and competition among users. Most existing works on this multiple networks sharing problem assume that users have the same utility functions, which neglect the fact that users may have diverse demand resulted from different applications, user preference etc., in reality. The diversity in user demands makes the original network selection problem even challenging that lightweight optimization methods cannot be directed applied. Aiming at maximizing the social welfare of users, we propose a local improvement algorithm, which does not rely on any centralized coordinator or global information compared to most of traditional schemes. Under a novel user-network association game formulation, we prove the proposed algorithm can converge to the suboptimal or optimal user-network associations, where the best equilibrium corresponds to the optimal user-network association. Finally, simulations are conducted to validate the convergence and performance of the local improvement algorithm.