Coordinated punishment occurs when punishment requires a specific number of punishers to be effective, otherwise, no damage will be inflicted on the target. While societies often rely on this punishment device, its benefits are unclear compared to uncoordinated punishment, where punishment decisions are substitutes. In this paper, we compare the efficacy of coordinated and uncoordinated punishment in a team investment game with two investors and one allocator. Our findings indicate that coordinated punishment results in higher levels of cooperation and reciprocity, as measured by the levels of joint investment and the return by allocators. Importantly, this does not translate into higher payoffs: investors use punishment more frequently when this is coordinated, which destroys the efficiency gains generated by the highest investment. In fact, our results suggest that the highest level of efficiency would be achieved if investors were not allowed to punish.

当惩罚需要特定数量的惩罚者才能有效时，就会出现协同惩罚，否则不会对目标造成伤害。虽然社会经常依赖这种惩罚手段，但与不协调的惩罚相比，它的好处尚不清楚，在不协调的惩罚中，惩罚决定是替代性的。在本文中，我们比较了两名投资者和一名分配者的团队投资博弈中协调和不协调惩罚的效果。我们的研究结果表明，协调一致的惩罚会带来更高水平的合作和互惠，这可以通过联合投资和分配者的回报水平来衡量。重要的是，这并不能转化为更高的回报：当协调一致时，投资者会更频繁地使用惩罚，这会破坏最高投资所产生的效率收益。事实上，我们的结果表明，如果不允许投资者进行惩罚，就能实现最高水平的效率。