Stability routing algorithm in MANETs aims at constructing routes with longer lifetime. But for the in-between nodes need to rebroadcast more RREQs to discover more stable routes, it also leads to a higher routing overhead. To release this problem, an overhead-adaptive scheme is proposed in this paper. In this scheme, a game is played among the in-between neighbor nodes when they receive the same RREQ. Based on the game, each neighbor node can get a probability to determine whether the received RREQ is allowed to rebroadcast. The simulation results show that this proposed scheme can reduce routing overhead obviously.