This paper explores the influence of two competing stubborn agent groups on the opinion dynamics of normal agents. Computer simulations are used to investigate the parameter space systematically in order to determine the impact of group size and extremeness on the dynamics and identify optimal strategies for maximizing numbers of followers and social influence. Results show that (a) there are many cases where a group that is neither too large nor too small and neither too extreme nor too central achieves the best outcome, (b) stubborn groups can have a moderating, rather than polarizing, effect on the society in a range of circumstances, and (c) small changes in parameters can lead to transitions from a state where one stubborn group attracts all the normal agents to a state where the other group does so. We also explore how these findings can be interpreted in terms of opinion leaders, truth, and campaigns.

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