WiMAX delivers Quality of Service (QoS) to users based on a pre-determined traffic classification model. We develop an auction framework to bid for allocating the resources based on the utilities and traffic demands. We classify the users into two categories Premium User who has a high priority access and Non premium user having low-priority access. In principle larger the bandwidth more resources WiMAX can support for the user traffic. We apply the concept of Incentive compatibility and use bidding mechanism to maximize the revenue and social welfare of the WiMAX networks. We have considered different cases to achieve this. First, Dependency of networks sharing the resources based on the concept of reduction to a maximum matching in weighted graphs. Second, Independency of networks with which it will share its resources. This is done by designing a Maxmin fairness algorithm with two different segments in a decision making process: (a) A time dependent function that considers the time when packets wait in queues; (b) A Buffer utility function to consider buffer size in scheduling to prevent overflow and proportional fairness scheme to gives a fair share to users and maximize the social welfare and revenue. Finally we simulate a seven cell approach in Opnet-WiMAX simulator for VoIP, FTP and HTTP traffic with different QoS requirements and show premium users gets prioritized access.