In many multi-agent scenarios, agents must balance both local and global performance and collaboration objectives with the constraints of efficient resource utilization. Here, consensus problems with fixed communication graphs are considered, where agents strive to reach a common decision value in minimum time while simultaneously minimizing a performance cost that measures the deviation of the decision value from the desired value. The paper offers preliminary results on the selection of meaningful decision values that approximate optimal solutions. The proposed approach shows a fast convergence time and also reduces the overall number of information transmissions by the agents in the network.

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