Kurokawa Shun
Graduate School of Agriculture, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan; Institute of Zoology, Chinese Academy of Sciences, Datun Road, Chaoyang, Beijing 100101, PR China.
Math Biosci. 2016 Dec;282:16-20. doi: 10.1016/j.mbs.2016.09.012. Epub 2016 Sep 28.
Cooperation is a mysterious phenomenon which is observed in this world. The potential explanation is a repeated interaction. Cooperation is established if individuals meet the same opponent repeatedly and cooperate conditionally. Previous studies have analyzed the following four as characters of conditional cooperators mainly. (i) niceness (i.e., when a conditional cooperator meets an opponent in the first place, he (she) cooperates or defects), (ii) optimism (when a conditional cooperator meets an opponent in the past, but he (she) did not get access to information about the opponent's behavior in the previous round, he (she) cooperates or defects), (iii) generosity (even when a conditional cooperator knows that an opponent defected in the previous round, he (she) cooperates or defects) and (iv) retaliation (a conditional cooperator cooperates with a cooperator with a higher probability than with a defector). Previous works deal with these four characters mainly. However, these four characters basically have been regarded as distinct topics and unified understanding has not been done fully. Here we, by studying the iterated prisoner's dilemma game (in particular, additive games) and using evolutionarily stable strategy (ESS) analysis, find that when retaliation is large, the condition under which conditional cooperators are stable against the invasion by an unconditional defector is loose, while none of "niceness", "optimism", and "generosity" makes impact on the condition under which conditional cooperators are stable against an invasion by an unconditional defector. Furthermore, we show that we can understand "niceness", "optimism", and "generosity" uniformly by using one parameter indicating "cooperative", and when the conditional cooperators have large "retaliation" enough to resist an invasion by an unconditional defector, natural selection favors more "cooperative" conditional cooperators to invade the resident conditional cooperative strategy. Moreover, we show that these results are robust even when taking the existence of mistakes in behavior into consideration.
合作是一种在这个世界上被观察到的神秘现象。其潜在的解释是重复互动。如果个体反复遇到同一个对手并进行有条件的合作，合作就会建立起来。先前的研究主要分析了作为有条件合作者特征的以下四个方面。（i）友善（即，当一个有条件合作者首次遇到一个对手时，他（她）选择合作还是背叛），（ii）乐观（当一个有条件合作者过去遇到一个对手，但他（她）没有获得关于对手上一轮行为的信息时，他（她）选择合作还是背叛），（iii）宽容（即使一个有条件合作者知道对手在上一轮背叛了，他（她）选择合作还是背叛）以及（iv）报复（一个有条件合作者与合作者合作的概率高于与背叛者合作的概率）。先前的研究主要涉及这四个特征。然而，这四个特征基本上一直被视为不同的主题，尚未得到充分的统一理解。在这里，我们通过研究重复囚徒困境博弈（特别是加法博弈）并使用进化稳定策略（ESS）分析，发现当报复程度较大时，有条件合作者对无条件背叛者的入侵保持稳定的条件较为宽松，而“友善”“乐观”和“宽容”这三个特征对有条件合作者对无条件背叛者的入侵保持稳定的条件均无影响。此外，我们表明可以通过使用一个表示“合作性”的参数来统一理解“友善”“乐观”和“宽容”，并且当有条件合作者具有足够大的“报复”能力以抵抗无条件背叛者的入侵时，自然选择更倾向于更“合作”的有条件合作者来入侵现有的有条件合作策略。而且，我们表明即使考虑到行为中存在错误，这些结果仍然是稳健的。
