From the viewpoint of game theory, this paper proposes a model that combines QoS index with price factor in overlay access networks, and uses the multinomial logit (MNL) to model the choice behaviour of users. Each service class is considered an independent and competitive entity offered by each provider,which aims at maximizing its own utility. Based on noncooperative game, we prove the existence and uniqueness of equilibriums between QoS levels and prices among various service classes, and demonstrate the properties of equilibriums. Finally, these results are verified via numerical analysis.