Department of Value and Decision Science, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro, Tokyo 152-8552, Japan.
Department of Value and Decision Science, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro, Tokyo 152-8552, Japan; Department of Innovation Science, Tokyo Institute of Technology, 2-12-1, Ookayama, Meguro, Tokyo 152-8552, Japan.
J Theor Biol. 2018 Aug 14;451:46-56. doi: 10.1016/j.jtbi.2018.04.019. Epub 2018 Apr 28.
Our society is based on group cooperation, but this remains an unsolved problem from the viewpoint of evolutionary biology and the social sciences. Group cooperation is often studied through the public goods game, and it has been shown that large group size never promotes the evolution of cooperation. We consider the mutual-aid game, in which one member of the group is chosen randomly as the aid recipient, and other members decide whether to help the recipient. This game can describe the early stage of insurance provision in England, for example. With reference to existing indirect reciprocity studies, we investigate what promotes the evolution of cooperation in the mutual-aid game by means of replicator equations and agent-based simulations. Our key findings are as follows. In a multilateral relationship in which members play the mutual-aid game in a group whose size is greater than two, once two or more defectors are in bad standing, they remain bad under the rule that a donor's bad reputation remains bad, whether or not the donor helps a recipient with a bad reputation. Then, cooperators never help them, and mutation helps the invasion of rare cooperators more when the group size is larger in the finite population, even when implementation and perception errors occur. Meanwhile, this rule never helps the invasion in the bilateral relationship in which the group size is two. Our results suggest that large group cooperation can be sustainable if social institutions are equipped with systems such as those in the mutual-aid game.
我们的社会是建立在群体合作基础上的，但从进化生物学和社会科学的角度来看，这仍然是一个尚未解决的问题。群体合作通常通过公共物品博弈来研究，研究表明，群体规模越大，合作的进化就越不可能。我们考虑了互助博弈，在这种博弈中，群体中的一个成员被随机选为援助接受者，而其他成员则决定是否帮助接受者。这个游戏可以描述英国早期的保险提供情况。参考现有的间接互惠研究，我们通过复制者方程和基于主体的模拟来研究互助博弈中合作进化的促进因素。我们的主要发现如下。在一个多边关系中，成员在一个大于两个成员的群体中玩互助博弈，一旦两个或更多的背叛者处于不良状态，只要捐赠者的坏名声保持坏名声，无论捐赠者是否帮助有坏名声的接受者，他们都会保持不良状态。然后，合作者永远不会帮助他们，而且在有限的种群中，当群体规模较大时，即使存在执行和感知错误，突变也会帮助稀有合作者的入侵，这比在双边关系中帮助更多。我们的研究结果表明，如果社会制度配备了互助博弈等系统，大型群体合作就可以持续。
