P Hauser Oliver, A Nowak Martin, G Rand David
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA.
Program for Evolutionary Dynamics, Harvard University, Cambridge, MA, USA; Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA, USA; Department of Mathematics, Harvard University, Cambridge, MA, USA.
J Theor Biol. 2014 Nov 7;360:163-171. doi: 10.1016/j.jtbi.2014.06.041. Epub 2014 Jul 8.
It has been argued that punishment promotes the evolution of cooperation when mutation rates are high (i.e. when agents engage in 'exploration dynamics'). Mutations maintain a steady supply of agents that punish free-riders, and thus free-riders are at a disadvantage. Recent experiments, however, have demonstrated that free-riders sometimes also pay to punish cooperators. Inspired by these empirical results, theoretical work has explored evolutionary dynamics where mutants are rare, and found that punishment does not promote the evolution of cooperation when this 'anti-social punishment' is allowed. Here we extend previous theory by studying the effect of anti-social punishment on the evolution of cooperation across higher mutation rates, and by studying voluntary as well as compulsory Public Goods Games. We find that for intermediate and high mutation rates, adding punishment does not promote cooperation in either compulsory or voluntary public goods games if anti-social punishment is possible. This is because mutations generate agents that punish cooperators just as frequently as agents that punish defectors, and these two effects cancel each other out. These results raise questions about the effectiveness of punishment for promoting cooperation when mutations are common, and highlight how decisions about which strategies to include in the strategy set can have profound effects on the resulting dynamics.
有人认为，当突变率很高时（即当个体参与“探索动态”时），惩罚会促进合作的进化。突变维持着惩罚搭便车者的个体的稳定供应，因此搭便车者处于劣势。然而，最近的实验表明，搭便车者有时也会花钱惩罚合作者。受这些实证结果的启发，理论研究探索了突变体罕见情况下的进化动态，并发现当允许这种“反社会惩罚”时，惩罚并不会促进合作的进化。在这里，我们通过研究反社会惩罚对更高突变率下合作进化的影响，以及通过研究自愿和强制公共品博弈，扩展了先前的理论。我们发现，对于中等和高突变率，如果存在反社会惩罚的可能性，那么在强制或自愿公共品博弈中增加惩罚都不会促进合作。这是因为突变产生的个体惩罚合作者的频率与惩罚背叛者的个体一样高，这两种效应相互抵消。这些结果引发了关于在突变普遍存在时惩罚促进合作有效性的问题，并突出了关于在策略集中纳入哪些策略的决策如何能对结果动态产生深远影响。
