A synergy of punishment and extortion in cooperation dilemmas driven by the leader

Abstract Punishment and extortion have been acknowledged to play key roles in sustaining and catalysing cooperation respectively, yet we still have to face a rather gloomy evolutionary outlook if we continue using them alone in a high betrayal temptation. This paper proposes a new strategy that combines punishment and extortion used by one leader. The results show that a node with a large degree is more capable of influencing others. Using the combined strategy, one large degree node could push everyone's mutual cooperation in a probability close to or equal to 1. Moreover, he/she obtains the highest scores. We also demonstrate that the combined strategy is superior to some classic winning strategies (WSLS). The findings show the synergy of punishment and extortion is effective in promoting cooperation. An immediate implication is that it combines two strategies’ merits, and the leader can choose the right strategy between them at the right time to fight the defectors. And the results are robust to game betrayer temptation, competitive strategies. Complementary, it has strong flexibility for the user.

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