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In wireless mesh network (WMN), multiple service providers (SPs) can cooperate to share resources (e.g., relay nodes and spectrum), to serve their collective subscribed customers for better service. As a reward, SPs are able to achieve more individual benefits, i.e., increased revenue or decreased cost, through efficient utilization of shared network resources. However, this cooperation can be realized only if fair allocation of aggregated payoff, which is the sum of the payoff of all the cooperative SPs, can be achieved. We first formulate such cooperation as a coalitional game with transferable utility, specifically, a linear programming game, in which, each SP should obtain the fair share of the aggregated payoff. Then we study the problem of allocating aggregated payoff which leads to stable service coalition of SPs in WMN based on the concepts of dual payoff and Shapley value.