This paper proposes a six-degree-of-freedom (6-DOF) control allocation strategy based on population game theory to address actuator redundancy and resource coordination in on-orbit cooperative manipulation using cellular satellite swarms. Firstly, a coupled attitude-orbit dynamic model is formulated via dual quaternion representation, and a generalized PD controller is designed for full-state regulation. Then, multi-objective fitness functions are constructed considering energy consumption, maximum output, and residual performance margins to evaluate actuator strategies. The control allocation is modeled as a population game, where allocation coefficients reflect strategy quality and satellite units act as dynamic candidates. Finally, a hierarchical control-allocation framework is developed to prioritize orbital thrust allocation, followed by coordinated torque distribution for attitude control. Simulation results verify the effectiveness of the proposed approach and demonstrate improvements in control accuracy and energy efficiency compared to conventional methods.