School of Knowledge Science, Japan Advanced Institute of Science and Technology, 1-Asahidai, Nomi, Ishikawa 923-1292, Japan.
Behav Processes. 2022 Nov;203:104754. doi: 10.1016/j.beproc.2022.104754. Epub 2022 Sep 28.
How cooperation could have evolved has been one of the central topics in evolutionary biology. When cooperators are likely to interact with other cooperators, and defectors are likely to interact with other defectors, positive assortment is created, facilitating the evolution of cooperation. Cooperation is observed not only in dyadic interactions but also, sometimes, in sizable groups. Previous studies have found that the opting out rule in which the group is disbanded if and only if the group is heterogeneous, especially facilitates the evolution of cooperation compared to the other opting out rules in multi-player games when the number of rounds is sufficiently large. However, the dynamics between the cooperators and defectors under such an opting out rule have been investigated only in the case where group size is relatively small (e.g., four). In addition, the effect of group size on the evolution of cooperation has not been explored, and considering that humans interact within larger groups, investigation in such large groups is essential. Here, through further algebraic analyses, it is newly revealed that there can be four internal equilibria when the group size is larger than four. In addition, while the effect of group size on cooperation is negative in the case of common goods, it is not straightforward (i.e., can be positive) in the case of public goods.
合作是如何进化的一直是进化生物学的核心课题之一。当合作者很可能与其他合作者相互作用，而背叛者很可能与其他背叛者相互作用时，就会产生正选择，从而促进合作的进化。合作不仅在二元相互作用中观察到，有时在相当大的群体中也观察到。先前的研究发现，在选择退出规则中，如果群体是异质的，群体就会解散，与多玩家游戏中的其他选择退出规则相比，特别是在轮数足够大的情况下，这种规则更有利于合作的进化。然而，在这种选择退出规则下，合作者和背叛者之间的动态仅在群体规模相对较小时（例如，四个）进行了研究。此外，群体规模对合作进化的影响尚未得到探索，并且考虑到人类在更大的群体中互动，在这种大群体中进行研究是必不可少的。在这里，通过进一步的代数分析，新发现当群体规模大于四时，可能存在四个内部平衡点。此外，当涉及公共物品时，群体规模对合作的影响并不直接（即可能是积极的），而当涉及共同物品时，群体规模对合作的影响是消极的。
