Situations in which immediate self-interest and long-term collective interest conflict often require some form of influence to prevent them from leading to undesirable or unsustainable outcomes. Next to sanctioning, social influence and social structure, it is possible that strategic solutions can exist for these social dilemmas. However, the existence of strategies that enable a player to exert control in the long-run outcomes can be difficult to show and different situations allow for different levels of strategic influence. Here, we investigate the effect of threshold nonlinearities on the possibilities of exerting unilateral control in finitely repeated n-player public goods games and snowdrift games. These models can describe situations in which a collective effort is necessary in order for a benefit to be created. We identify conditions in terms of a cooperator threshold for the existence of generous, extortionate and equalizing zero-determinant (ZD) strategies. Our results show that, for both games, the thresholds prevent equalizing ZD strategies from existing. In the snowdrift game, introducing a cooperator threshold has no effect on the region of feasible extortionate ZD strategies. For extortionate strategies in the public goods game, the threshold only restricts the region of enforceable strategies for small values of the public goods multiplier. Generous ZD strategies exist for both games, but introducing a cooperator threshold forces the slope more towards the value of a fair strategy, where the player has approximately the same payoff as the average payoff of his opponents.
翻译:直接的自我利益和长期的集体利益冲突往往需要某种形式的影响力,以防止它们导致不可取或不可持续的结果。除了制裁、社会影响和社会结构之外,还有可能存在战略解决办法来应对这些社会困境。然而,使行为者能够控制长期结果的战略可能难以显示,不同的情况允许不同程度的战略影响。在这里,我们调查门槛非线性对在有限的重复的正玩家公益游戏和滑雪游戏中实施单方面控制的可能性的影响。这些模式可以描述为创造利益而需要集体努力的情况。我们从协调者门槛的角度确定存在慷慨、敲诈勒索和平衡零非定期(ZD)战略的条件。我们的结果显示,对于两个游戏来说,门槛性标准防止ZD战略的均衡化。在滑雪游戏中,引入一个协调者门槛,对可行的敲诈ZD战略的区域没有影响。在公共游戏中,敲诈性战略的难度更大,只有可执行性游戏的最小值,只有其平均值的门槛。