A cooperative network model of sociological interest is examined to determine the sensitivity of the global dynamics to having a fraction of the members behaving uncooperatively, that is, being in conflict with the majority. We study a condition where in the absence of these uncooperative individuals, the contrarians, the control parameter exceeds a critical value and the network is frozen in a state of consensus. The network dynamics change with variations in the percentage of contrarians, resulting in a balance between the value of the control parameter and the percentage of those in conflict with the majority. We show that the transmission of information from a network $B$ to a network $A$, with a small fraction of lookout members in $A$ who adopt the behavior of $B$, becomes maximal when both networks are assigned the same critical percentage of contrarians.