In this work, the inter-linked problems of bandwidth allocation for wireless service providers (WSPs) and WSP selection for users in heterogeneous cellular networks (HCNs) are addressed by employing a multi-hierarchical game framework. Wherein, while the interaction between users are modelled using evolutionary game theory, the interactions between competing WSP's are modelled as a non-cooperative spectrum bandwidth allocation game (N-BAG). Moreover, the interaction between the WSPs and users is modelled as a multi- leader multi-follower Stackelberg game. After that, for the formulated evolutionary game, the existence and uniqueness of the evolutionary equilibrium (EE) was investigated. Conditioned on the obtained EE, the existence of a Nash equilibrium (NE) for the proposed N-BAG has been further proven and an offline algorithm to achieve the equilibrium state was proposed. Finally, simulation results verify the validity of our analysis and demonstrate that a unique NE would be achieved by the HCNs adopting the developed algorithm.