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In this paper, GTAP-BRM (game theoretic access probability based bandwidth request mechanism) is proposed for WiMAX PMP (point to multipoint) network. In the reference standard, IEEE 802.16, connections belonging to QoS (quality of service) class rtPS (real time polling service) are provisioned to issue BW-REQ (bandwidth request) in contention free way while nrtPS (nonreal time polling service) can issue in both contention based and contention free way. This proposed GTAP-BRM, however, offers feasibility to make BW-REQs for both these classes in contention based way. Connections belonging to QoS classes with stringent delay requirement always desire very high average success probability and very low average access delay for the BW-REQs made, if contention based BW-REQs are to be made. This proposed GTAP-BRM caters these requirements for rtPS conncetions with almost 100% average success probability yielding average access delay of around 1 frame-length time. The price paid for that achievement is lower average success probability with longer access delay for delay intolerant nrtPS connections.