This paper investigates a safe consensus problem for cooperative-competitive multi-agent systems using a differential privacy (DP) approach. Considering that the agents simultaneously interact cooperatively and competitively, we propose a novel DP bipartite consensus algorithm, which guarantees that the DP strategy only works on competitive pairs of agents. We then prove that the proposed algorithm can achieve the mean square bipartite consensus and $(p,r)$-accuracy. Furthermore, a differential privacy analysis is conducted, which shows that the performance of privacy protection is positively correlated with the number of neighbors. Thus, a practical method is established for the agents to select their own privacy levels. Finally, the simulation results are presented to demonstrate the validity of the proposed safe consensus algorithm.

differential privacy, safe consensus, cooperative-competitive multi-agent systems, Laplace distribution, $(p, r)$-accuracy

93A14, 93C10

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