The traditional vertical handover schemes postulate that vertical handover of each user comes on an individual basis. This enables the users to know previously the decision already made by other users, and then the choice will be made accordingly. However, in the case of a group vertical handover, almost all the VHO decisions - which will certainly choose the best network, will be made at the same time which will lead to system performance degradation or network congestion. In this paper, we propose a totally decentralized algorithm for network selection which based on the Congestion Game to resolve the problem of network congestion in GVHO. Therefore, the proposed algorithm named Fully Decentralized Nash Learning Algorithm with incomplete information is a prediction done by each mobile in the group that helps them to reach the Nash equilibrium. Simulation results validate the algorithm and show its robustness under two scenarios. In the first one, we examine the algorithm with a fixed number of mobiles in group to evaluate the mixed strategy and the average perceived throughput of mobiles in WIMAX and HSDPA on the basis of iteration. In the second one, we examine the algorithm with different number of mobiles in group for testing the average number of iterations needed to reach the Nash equilibrium. We also compare it with the traditional vertical handover algorithm.