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In this paper, we consider the problem of providing robustness to adversarial communication in multi-agent systems. Specifically, we propose a solution towards robust cooperation, which enables the multi-agent system to maintain high performance in the presence of anonymous non-cooperative agents that communicate faulty, misleading or manipulative information. In pursuit of this goal, we propose a communication architecture based on Graph Neural Networks (GNNs), which is amenable to a novel Gaussian Process (GP)-based probabilistic model characterizing the mutual information between the simultaneous communications of different agents due to their physical proximity and relative position. This model allows agents to locally compute approximate posterior probabilities, or confidences, that any given one of their communication partners is being truthful. These confidences can be used as weights in a message filtering scheme, thereby suppressing the influence of suspicious communication on the receiving agent's decisions. In order to assess the efficacy of our method, we introduce a taxonomy of non-cooperative agents, which distinguishes them by the amount of information available to them. We demonstrate in two distinct experiments that our method performs well across this taxonomy, outperforming alternative methods. For all but the best informed adversaries, our filtering method is able to reduce the impact that non-cooperative agents cause, reducing it to the point of negligibility, and with negligible cost to performance in the absence of adversaries.