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Fourth generation (4G) wireless networks will provide seamless high bandwidth connectivity with quality-of-service (QoS) support to mobile users where a mobile will be able to connect to several wireless access networks simultaneously. In such a scenario, bandwidth allocation to a mobile from different types of networks will depend on the traffic load characteristics in each access network. In this paper, we formulate the bandwidth allocation problem in a 4G heterogeneous wireless network as an oligopoly market competition. In an oligopoly market, a few firms provide service/product to the customers. Here, we model the firms as the different types of networks offering bandwidth to the connections in order to maximize the system utility. A Cournot game is used to model this market competition and Nash equilibrium is considered to provide a stable solution. We propose two algorithms, namely, iterative and search algorithms, to obtain the solution. Based on the proposed bandwidth allocation algorithm, we present an admission control mechanism to ensure that the QoS of new and ongoing connections are maintained at the target level.