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Multi-agent reinforcement learning systems deployed in real-world robotics applications face severe communication constraints that significantly impact coordination effectiveness. We present a framework that combines information bottleneck theory with vector quantization to enable selective, bandwidth-efficient communication in multi-agent environments. Our approach learns to compress and discretize communication messages while preserving task-critical information through principled information-theoretic optimization. We introduce a gated communication mechanism that dynamically determines when communication is necessary based on environmental context and agent states. Experimental evaluation on challenging coordination tasks demonstrates that our method achieves 181.8% performance improvement over no-communication baselines while reducing bandwidth usage by 41.4%. Comprehensive Pareto frontier analysis shows dominance across the entire success-bandwidth spectrum with area-under-curve of 0.198 vs 0.142 for next-best methods. Our approach significantly outperforms existing communication strategies and establishes a theoretically grounded framework for deploying multi-agent systems in bandwidth-constrained environments such as robotic swarms, autonomous vehicle fleets, and distributed sensor networks.