Evolutionary dynamics of memory-one extortion and generosity on scale-free simplices

Both extortionate and generous strategies within the framework of zero-determinant (ZD) strategy can be linearly related to the opponent's payoffs. Here we explore their evolutionary performances for both iterated two-player and multi-player games. We mainly investigate two scenarios on simplicial complexes: one is the evolutionary scenario with cooperation (C), defection (D) and extortion (E), the other is the cooperation, defection and generosity (G). We find that both extortion and generosity can help cooperators resist the invasion of defectors. Intriguingly, the extortioner, who always enforces higher payoff than co-players, is more beneficial to promote cooperation than generosity. Compared with kindness and indulgence, being strict with the co-players can actually maintain cooperative behaviors in the long run. Simulations on the simplicial complexes revel that the catalytic effect of extortion on the evolution of cooperation even be more obvious in iterated multi-player social dilemmas than the two-player case, hence cooperation becomes more popular when the networks include more 2-simplex interactions. Our results can help to illustrate the role of higher-order interaction in the evolution of altruistic behaviors.