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We consider a multi-agent linear quadratic optimal control problem. Due to communication constraints, the agents are required to quantize their local state measurements before communicating them to the rest of the team, thus resulting in a decentralized information structure. The optimal controllers are to be synthesized under this decentralized and quantized information structure. The agents are given a set of quantizers with varying quantization resolutions—higher resolution incurs higher communication cost and vice versa. The team must optimally select the quantizer to prioritize agents with ‘highquality’ information for optimizing the control performance under communication constraints. We show that there exist a sepatation between the optimal solution to the control problem and the choice of the optimal quantizer. We show that the optimal controllers are linear and the optimal selection of the quantizers can be determined by solving a linear program.