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The dynamic nature of mobile ad hoc networks (MANETs) is attributed to several inherent characteristics, such as variable link behavior, node movements and changing network topology. Providing quality of service (QoS) in such a dynamic environment is very difficult. QoS-aware routing is one of the QoS support that provides QoS at the network layer. In the presence of high mobility, this QoS solution can be down. Furthermore, taking mobility in consideration can enhance and guarantee it. In this paper, we propose a cooperative game theory approach to extract a core in MANET that is stable in terms of mobility. This core is a subset of MANET mobile nodes where his mobility is less and stable. The selection of paths by the QoS-aware routing protocols through this extracted core can be ensure more the provided QoS in time.