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LTE standard defines strict requirements for service classes in order to provide end users with exceptional QoS characteristics including fast connectivity and high data rates. However there is no standard scheduling algorithm defined for LTE and the task of protecting end user satisfaction while maintaining service class restrictions is left upon the service provider and currently is an open issue. To address this challenge, in this work we proposed a two-level scheduler with a utility based game theoretic application in the first level that distributes physical resource blocks among classes with different QoS requirements and a delay based air interface scheduling algorithm in the second level that satisfies the strict levels of delay budget requirements defined for LTE classes. A cooperative game is formed between different service class flows by use of a sigmoid utility function that allows for distribution of resources. Lagrangian formulation is used to find the associated Pareto Optimality. The delay based scheduler checks each user's packet delay in its respective service class and makes scheduling decisions in the downlink direction utilizing current channel conditions. Simulation results carried out with key performance matrices including throughput, packet loss ratio, system delay and fairness index proved the usefulness and efficacy of the proposed approach as compared to existing Proportional Fair, Exponential Rule and M-LWDF algorithms.