在背部额叶皮层中复杂社会决策的基础功能

　　我们总共进行了四项研究：一项社会功能磁共振成像实验（研究1 ，n = 56；图3）；行为实验（研究2
，n = 795;图4）;对照fMRI实验（研究3，n = 32;图5）;和补充行为实验（研究4 ，n = 1,022；扩展数据图5）。所有研究都使用了相同实验范式的变体 。 　　最初有59名社会功能磁共振成像实验的参与者（研究1）
。但是
，两个参与者没有完成扫描课程，一名参与者在实验中反复入睡。这些从样本中删除 ，因此最终样本包含56名参与者（年龄范围18-38岁，其中33名女性） 。参与者因参加实验而获得了50英镑的收入
，以及根据其在任务中的表现分配的额外收入
。牛津大学伦理委员会批准了这项研究，所有参与者均提供了知情同意书（MSD参考编号：R60547/RE001）。 　　在实验程序开始时 ，在进入MRI扫描仪之前
，参与者进行了行为实验 。他们被告知，实验前的目的是在感知决策任务（随机点运动任务54）中记录其表现的绩效评估 ，并且该绩效将在随后的FMRI实验中使用。的确如此
，实验程序不涉及欺骗
。我们使用自动化的计算机算法将参与者的记录性能与以前的三名参与者的表现相结合。在实验前之后使用该算法来创建实验时间表，并确保在参与者之间进行实验时间表是可比的 ，并且在某些关键特征方面保持平衡（例如
，四个参与者中的每个玩家中的每个玩家都具有大致相似的性能），并且与关键的兴趣变量（例如 ，跨玩家估计的绩效估计）相关 。为了确保仔细的平衡
，鉴于主要fMRI实验中的试验数量，参与者进行了比必要的更多试验 ，从而使算法可以反复进行亚样本表现，直到达到了时间表的上述关键标准
。参与者进行了预示前后
，我们使用了计划生成算法，但在他们进入MRI扫描仪之前。这些时间表包括参与者的垂直表演 ，然后将其他三名玩家转移到操作MRI实验的计算机上 。每个实验中其他三个玩家的表现（合作伙伴和两个对手）是从以前参与者的日志文件中获取的
。对于fMRI实验的前几位参与者（如果没有前面的参与者）
，这些日志文件来自参加试点实验的参与者。fMRI实验持续了大约60分钟 。之后，参与者被汇报 ， 填写了一些与当前研究无关的问卷
，并离开了
。 　　使用PsychToolBox-3在MATLAB中对扫描和fMRI实验之前进行的行为预示（Ref。55; http://psychtoolbox.org）进行了编程 。为了呈现随机点运动刺激，我们使用了变量相干随机点运动工具箱（版本2; https：//shadlenlab.columbia.edu/resources/vcrdm.html）
。 　　在实验前 ，参与者判断了随机点运动运动学（RDK）刺激的运动方向。参与者按下左或右按钮
，以指示RDK刺激的左侧或向右运动指示 。参与者意识到，他们将以不同水平的连贯性执行这些运动判断 ，从而使RDK刺激的检测更加容易或更加困难。实验前的运动相干构成了972次RDK试验
，使用3.2％，12.8％和25.6％的运动相干
。将每个RDK刺激呈现为0.45 s ，并且在RDK偏移后必须在0.6 s内做出有效响应。在这个时间窗口中未能做出响应是不正确的性能，并由“错过！ ”表示 。屏幕上的消息
。参与者知道这一点
，并被指示避免错过试验。重要的是，参与者没有获得RDK方向判断的性能反馈（错过的试验除外） 。这样做的原因是 ，参与者将在随后的FMRI实验中见证并了解他们记录的
，垂直的表现，因此在实验的早期 ，请不要向他们提供此信息很重要
。预先经验大约需要25分钟。 　　我们采取了几项措施来简化参与者的主观经验方面的实验和随后的fMRI决策实验 。首先
，参与者进行了一些实验前的练习试验，在这些试验中 ，他们得到了明确的性能反馈
，并且这种反馈是使用相同的提示提示的，这些提示也表明在主要的fMRI实验中成功且错误的性能（成功性能的黄色硬币 ，用于绩效
，是红色的X，而红色的X则是反对性能的）
。对于参与者而言 ，这项措施强调了一个事实，即在fMRI扫描期间提出的绩效指数与参与者在实验前时期的表现有关。其次
，在实验前，参与者以序列进行了六项RDK试验的序列 ，然后进行1 s的间隔间隔 。试验的阻止与以下事实相对应：在fMRI实验中
，参与者在每个试验中都观察到每个参与者连续六个性能提示的快速性能序列
。因此，再次采取了这项措施 ，以使参与者的实验经验与主要的fMRI实验相结合。第三
，在整个体验期间，屏幕的布局与主fMRI实验的屏幕相似 。提到SEX ，合作伙伴和两个对手的提示是在屏幕上分发的
，每个玩家都占据了最左翼，右上 ，左下或右下角的位置。这些提示位置在实验前和主要fMRI实验中是相同的
。他们在整个实验过程中为每个参与者保持了固定
，但是他们在参与者之间是随机和平衡的，并限制了伴侣的位置始终与自我位置相邻（例如 ，自我和伴侣可以占据两个上位置，例如
，两个左侧位置）。在实验期间，大多数时间都没有显示自我提示 。反而 ， 参与者看到RDK刺激被要求在此位置做出回应
。但是
，尽管与预先体验期间执行的任务无关，但表明其他三名球员的提示在整个前体验中得到了展示。该措施用于在实验期间表明参与者的表演将与其他三名球员在主要fMRI实验中的表现配对 ，并演示了团队配对（自我和伴侣与两个对手） 。因此
，这项措施再次有助于确保参与者在实验前和主要fMRI实验中的经历相似
。 　　最后，在实验前和主要fMRI实验中 ，我们都使用静态RDK图像作为指示玩家身份的提示
，并且这些提示固定在特定的屏幕位置（请参阅上点）。RDK可以通过其空间位置，颜色（白色 ，绿色
，橙色或紫色）以及两个字母（例如参与者的缩写，例如MW ，for self for self，for pa for pain for for Partern和o1 and O2） 。静态RDK图像象征着每个玩家的性能提示均来自其Veridical RDK的性能
。这样做是为了提醒参与者在主要功能磁共振成像实验中的参与者
，他们观察到的表演是从RDK预先体验中获得的。总而言之，采取了一些措施向参与者说明他们的实验前绩效评估无缝地进入了主要的fMRI实验中 ，并且他们的绩效在两个竞争团队的社会环境中很重要 。 　　FMRI的主要实验涉及完成记忆引导的社会决策任务
。每个试验都构成了一个观察阶段和一个决策阶段
，在该阶段中，参与者就记忆中观察阶段中提供的信息做出了决策。当球员分为两支球队时 ，有四个球员的表现在fMRI实验中是相关的：参与者自己的表现（自助
，S），伴侣的表现（PA）和两个对手的表现（O1和O2） 。在整个实验过程中 ，团队成员资格一直是不变的
，并且由实验者预定。没有提供有关其他玩家的更多信息（例如他们的性别或年龄）
。 　　在观察阶段，参与者以随机但反平衡的顺序观察每个玩家的性能提示（例如 ，每个玩家在序列中首先出现在相同数量的试验中）。参与者来自预先体验的垂直表现与其他三名参与者的垂直表演配对
，并在此阶段展示 。对预录的性能的见解与在主要实验中击败另一个团队无关（扩展数据图2）
。玩家的身份是通过RDK图像提示的，并以与实验前相同的空间位置显示 ，以增强实验前和主fMRI实验之间的连续性，并说明所涉及的表演的表现
，指的是经过实验性绩效评估。 　　在观察阶段，对于每个玩家 ，参与者都观察到六个简短的表现提示 。性能提示总是在每个玩家的同一位置的屏幕上集中显示
，并且成功的表演由黄色的硬币提示表示，并且由红色X表示错误的表演
。参与者已经知道了从前体验的这些提示的含义（请参阅“行为预先体验预先体验
”部分）。由于性能提示始终出现在所有玩家的同一位置 ，因此我们向玩家提出了以下方式相关的这些表演：在性能提示序列开始之前的400毫秒之前
，相应玩家的RDK图像在其预定义的位置出现在其预定义的位置，其点在其速度上以缓慢而连贯的方式以2.1 s的方式移动 。重要的是 ，主动RDK只是指示相关播放器的一种手段
。 　　这次的参与者不必辨别点的运动方向（这很容易
，因为RDK的连贯性很高）。他们只需要了解表现出的性能提示以中央表示该特定玩家的性能 。与本研究中的许多其他小型操作一样，使用移动的RDK表明相关玩家是一种使参与者能够在实验前和主要fMRI实验之间建立联系的方法 ，并且可以使显示的与各自玩家的RDK表现相关的显示性能提示是合理的
。当玩家的RDK移动时
，六个性能提示的序列在屏幕上集中显示。在上述400毫秒上述400毫秒之后，提出了200 ms的第一个性能提示 。随后显示了其余的性能提示 ，它们之间的延迟为100毫秒，每个延迟也为200 ms。在此期间
，播放器的RDK仍然活跃以指示相关播放器，而RDK运动在六个性能提示的序列也结束时就完全结束了
。 　　对于四个球员中的每一个 ，表演提示都是以这种方式呈现的。在特定于播放器的RDK处于活动状态时
，显示了一系列六个中心呈现的性能提示 。介绍了玩家的表现后，他们的RDK停止移动并保持静态 ，直到决策阶段开始
。这意味着
，在性能阶段结束时，所有四个RDK都静态显示在与各自播放器相关的位置的屏幕上。重要的是 ，球员的顺序完全平衡（图2） 。最后
，在显示最后一个球员的表现并在泊松分布的抖动（1-5 s，平均为2 s）之后结束了观察阶段 ，决策阶段开始了
。 　　在每个试验中
，在观察阶段出现了决策阶段。在决策阶段，参与者比较了在上一个观察阶段显示的玩家之间的性能得分 。这个决定是在自己的团队的相关成员中表现得更好 ，还是对手团队的相关成员的表现更好
。直到决定开始之前，必须比较哪些球员。因此
，参与者必须记住所有球员的表现得分，即成功表现的数量 。每个球员的表现分数在0到6之间（如果表现不佳或分别取得成功 ，则必须从六个表演提示中提取
，这些六个性能提示是在该玩家的RDK处于活动状态的同时所显示的（通过积累黄色的成功提示并丢弃红色错误线索）
。重要的是，每个决策阶段实际上构成了两个决策 ，并且都提到了在试验阶段刚刚看到的相同表现。这两个决定均遵循完全相同的逻辑
，这就是为什么仅在图1中显示了其中的第一个 。请注意，做出了两个决定 ，并且都提到相同的信息
，这意味着人们必须在整个审判中记住所有四个球员的表现，除了第一个决定之外 ，直到做出第二个决定。 　　在观察阶段之后的时间抖动之后
，决策阶段开始提出箭头提示，该箭头表明在决策中要比较哪些玩家
。球员的团队成员资格限制了哪些决定。可能有三种可能的决策类型 。在自我决定中 ，将参与者自己的表现与两个对手之一的表现进行了比较（每个对手经常）
。必须忽略其他两个球员（伴侣和无关的对手）的表现。在合作伙伴的决定中，将伴侣的表现与两个对手之一的表现进行了比较（每个人经常经常）
，而忽略了自我的表现和其他无关的对手 。最后，在小组决策中 ，比较了两组的性能总和
。箭头提示分别指向自我和相关的对手（自我决定）
，伴侣和相关对手（伴侣的决定）或在两组（小组决策）中指出了这些不同的决定。这意味着，对于自我和伴侣的决定 ，对手可以分为相关的对手（OR）和无关紧要的对手（OI）
，并且两个反对者对于自我和伴侣决定的相同数量的审判都是相关且无关紧要的 。相比之下，在小组决定中 ，两个对手都是相关的
。 　　决定是通过比较提示球员的表演来做出的。但是
，参与者还必须考虑非社会奖金 。该奖金是在指示相关参与者的决策箭头之上提出的
。奖金以黄色硬币和半币的形式显示，以获得积极的奖励 ，红硬币和半币的负数为负奖金。积极的奖励意味着必须为自己的团队表现增加积分
，而负数意味着必须为对手团队的表现增加积分 。在决策中包括奖金是有用的，因为这意味着参与者必须等到决策时间才能知道有关决定的所有信息。这确保参与者将在决策阶段而不是事先做出决定
。此外 ，奖金的值为-1.5，-0.5
，+0.5或+1.5。这很有用，因为这意味着每个试验中总是有正确的响应 。由于性能得分始终是整数 ，因此±0.5意味着
，即使表现分数相同，也必须将一支球队脱颖而出
。This meant that the full social decision variables (DV) for the self, partner and group were: DVself = S − Or + B, DVpartner = P − Or + B and DVgroup = S + P − O1 − O2 + B, where S indicates one’s own performance score (self performance), P indicates the partner’s performance score (P performance), Or indicates the relevant opponent’s performance score (Or performance), and O1 and O2 indicate the两个对手的表现得分（O1性能和O2性能）。请注意 ，这些标签用于小组决策
，或者是因为两个对手在小组决策中都相关 。 　　该决定是作为参与/避免使用两个按钮的决策6,25提出的
。决定是比较相关球员的表现（奖金中的货物），并指出自己的团队的相关成员在观察中表现更好 ，还是对手团队的相关成员的表现是否更好。决定参与意味着选择自己的团队
，在各自的按钮按下，这表明了一个大盒子在两个RDK周围出现的大盒子象征着自己的团队 。做出选择表明 ，自己的团队的相关成员的性能估计要比其他团队的相关球员更好（也包括在奖金中）
。参与选择的回报是该试验的Veridical DV。这意味着
，如果一个人自己的团队确实更好，并且DV是+2（有关DV计算的方程式） ，那么结果将为+2 。但是，如果选择可以参与
，并且DV是-1，则结果为-1
。相比之下 ，选择对手团队（做出避免选择）的结果总是会导致零的回报。这种报酬计划意味着做出正确选择以最大化试验的奖励结果总是有益的 。这意味着只有在自己的团队确实更好的情况下才能选择参与
，并且在避免丢失的情况下选择避免避免。关于是否做出正确选择的反馈
。在实验过程中积累了积分，并在实验结束时转化为少量额外的奖金支付。参与者还收到了一个额外的回报 ，该报酬与他们的合作伙伴在实验过程中收集了多少积分成正比 。后者是基于对伴侣进行FMRI决策实验时积累了多少要点的垂直读数
。 　　请注意
，在决策实验的背景下，自我和伴侣对任务同样重要。在实验时间表中 ，自我和伴侣的决定同样经常 。无论是合作伙伴审判还是自我试验
，从相同的DV试验中的回报都是相同的
。因此，估计合作伙伴的表现对成功执行任务的影响与正确估算自己的表现完全相同。 　　每个决定一直持续到回应 。之后 ，为0.5 s
，围绕自己的团队或对手团队的一个盒子指出，是否已经做出了订婚（围绕自己的团队围绕一个盒子的盒子）或避免做出决定（对手团队周围的盒子）
。在第一个决定之后 ，暂时的抖动为2-8 s（泊松分布，平均= 3.5 s）
，直到第二个决定开始。请注意，第二个决定不能与第一个决定相同的球员之间进行比较 。这意味着在小组决定之后 ，在同一审判中不可能做出另一个小组决定
。在用O1作为相关对手做出自我决定之后
，O2可能是相关对手的另一个自我决定（但不是另一个具有自我和O1的对手）。在第二次决定之后，审议间隔为1-5 s（平均= 2 s） ，然后开始了下一个试验 。 　　该实验包括144次试验。因此
，做出了288个决定，这些决定均匀地分布在自我决定 ，伴侣决策和小组决策之间
。如上所述
，通过使用算法从前体验生成时间表可确保为所有参与者的四个玩家中的每个参与者中的每一个都精确平衡表演。 　　一组三个顺序基础函数构成了我们研究中顺序决策空间的基础 。我们将一个矩阵W定义为包括基函数的三个行向量（W1，W2 ，W3）为W =（W1
，W2，W3）t ，其中T表示转型操作
。我们将在观察阶段观察到的顺序性能的投影表示为b =（b1，b2和b3）t。我们将顺序性能得分称为POS =（POS1
，POS2，POS3 ，POS4）t 。例如
，POS1是观察阶段序列中第一个玩家观察到的性能得分，而与身份无关
。在每个试验中 ，它是0到6之间的数字
，反映了汇总性能得分。必须从一系列性能提示中提取每个播放器的性能得分，这些性能提示表明为每个玩家提供了成功或错误的性能 。我们使用以下一组基础函数W1 ，W2和W3： 　　重量的位置表明在每个试验开始时呈现的表演顺序中
，各个玩家的顺序位置
。例如，W1（2）指的是序列中的第二名球员 ，他的重量为正。重要的是
，基础功能是顺序定义的，而不是在以代理为中心的参考框架中定义（后者对自己的团队使用积极的迹象 ，对对手的团队使用负面标志） 。对基础函数的投影是权重矩阵的点产物和顺序性能得分：b = wpos（有关示例计算，请参见主文本和图2）
。这意味着基本功能预测被定义为： 　　三个基础函数（W1
，W2，W3）具有两个重要特征。第一个是它们是成对的正交 ，第二个是所有组和二元重量向量都可以从它们中得出（也就是说
，它们在我们任务中构成了顺序决策空间的基础）； 　　这三个基础函数构成了顺序决策空间的基础，这意味着我们的实验设计提供的所有可能的顺序比较都可以与它们定义 。首先 ，三个权重矢量W1
，W2和W3已经代表了在连续参考框架中做出的所有可能的组决策。这意味着他们捕获了两个球员组成的球队的所有可能的配对，并带有一个积极的迹象 ，还有一个由四名玩家序列的其他两个球员组成的球队
。请注意
，权重向量的总体迹象是任意的（例如，是[1 ，1
，-1，-1 ，-1]还是[-1，-1
，-1，1 ，1]）
，因为我们只关心比较本身，无论是团队是自己的团队还是对手的团队。倒对比度可以很容易地通过用-1乘法来构造 ，因此从这里的对比列表中省略了（例如
，[-1，-1 ，1
，1，1] = -1×[1 ，1
，1，-1 ，-1，-1]） 。 　　二元重量向量要求参与者忽略两个球员
，并比较每队一个球员
。因此，它们表示为对比度 ，例如[0
，1，-1 ，0]
，其中包含两个零（无关的玩家），一个正面和一个负重（比较相关的玩家）。例如 ，对比度[0
，1，-1 ，0]表示必须将序列中第二个时间点显示的性能与序列的第三个性能进行比较（POS2对POS3） 。同样
，可以通过用-1乘法来轻松构建倒二元重量向量（例如[0，-1 ，1，0]）
。关于二元比较
，以下是所有可能的顺序二元重量矢量的完整列表，以及这些比较如何是基础函数W1 ，W2和W3的线性组合。同样
，我们省略了签署的对比 。请注意，对比的编号对应于主文本（见图2）
。 　　由于这些原因 ，W1
，W2和W3构成了本实验中所有顺序决策对比的正交基础。就像三个基础函数W1，W2和W3足以定义本任务上下文中所有相关的顺序比较一样 ，对基本函数的投影也足以计算实际的性能差异（与这些对比相关的决策变量） 。请注意
，参与者还考虑了非社会奖金以及此顺序决策变量（请参阅“决策阶段”部分）
。由于权重向量W1至W9定义了所有可能的顺序比较，因此与这些对比相关的DV可以计算为： 　　具体而言 ，这意味着： 　　基本函数可以轻松地从观察到的性能序列中得出顺序的决策变量。可以根据相关性对基础函数进行排序 。我们将主要基础函数定义为在观察阶段在四个玩家序列中与两个团队的分组相吻合的函数。对主要基础函数的投影是组决策的顺序DV
。次级函数被定义为与主要基础函数结合的另一个基础函数导致当前相关的二元决定。仅针对二元决定定义次级函数
，仅在揭示该决定后才知道 。最后，将第三级函数定义为与当前二元决策无关的剩余基础函数
。 　　要达到以代理为中心的DV ，主要和次要函数都必须在两个团队的参考范围内。如果已经是这样的，则以代理为中心的决策变量是主要和次要函数的简单线性添加（加上非社会奖励） 。但是
，有时必须将基础函数倒置以与以代理为中心的观点保持一致
。我们将其称为符号倒置，并指将基本函数从连续的参考框架转换为以代理为中心的社会参考框架作为基础功能投影的反转的过程。关于主要基础功能 ，这意味着相应的权重矢量的权重必须符合玩家身份
，并将正权重分配给自己的群体的玩家，而负重为对手组的负重 。因此 ，以代理为中心的主要预测独立于任何序列信息
，并且只是为自己的团队分配了积极的权重，而负重为对手的团队
。因此 ，以代理为中心的主要基础功能捕获了自己的团队之间的性能差异。请注意
，我们研究主要和次级功能投影的神经分析包含这些相同的基础功能预测，但在此以代理为中心的参考框架（倒置）中进行了转换 。 　　还需要将次级函数转换为以代理为中心的空间 ，以达到以代理为中心的DV进行二元决定
。以与以代理为中心的主要基础功能相同的方式
，以代理为中心的二级函数从一个人组中为相关玩家分配了正权重，而对手组的相关玩家负重为负权重。但是 ，与以代理为中心的主要基础功能不同，以代理为中心的二级基础功能从一个人的群体中分配了负重的负重
，而对对手团队的无关球员的体重则为无关紧要 。例如，在自我试验中 ，需要以下一组权重做出正确的决定： 　　此比较的倒置（即以代理为中心的社会）和次级体重向量为： 　　请注意
，同样，在这些方程式中 ，向量内的位置并不是指观测阶段的顺序位置
，而只是表示玩家的身份。通过这种方式，无关紧要的玩家在线性结合两个以代理为中心的基础函数时取消（与图3中给出的示例进行比较）
。例如 ，对于自我决定
，伴侣和对手之一是无关紧要的： 　　由于点产品对向量添加进行分配（请参阅“基础函数及其权重矢量 ”部分），因此 ，当将平均值一起提供时
，主要和次要的预测为二元决策提供了一个简单的途径（请注意，仍然需要添加非社会性刺激性 ，并且在所有分析中都需要添加这一点）。 　　使用具有64通道头线圈的3-Tesla Siemens MRI扫描仪获取成像数据 。以3.97毫秒的回声时间（TE），1.9 s的重复时间（TR）和1 mm×1 mm×1mm的体素大小收集T1加权结构图像
。使用多播T2*加权的回声平面成像序列收集功能图像
，其加速度为两个，TE = 30 ms ，TR = 1.2 s
，VOXEL大小为2.4 mm×2.4 mm×2.4 mm×2.4 mm，60°的角度 ，一个60°flip角
，视野的视野216 mm和60毫米和60 slies每体积。大多数扫描数据的倾斜角度与PC -AC线的倾斜角度为30°，以避免轨道额外区域中的信号脱落56 。还采用了两次田间图扫描（序列参数：TE1 ，4.92 ms; TE1
，7.38 ms; TR，4482 ms; flip角 ，46°; Voxel尺寸
，2 mm×2 mm×2 mm）的B0场还被获取并用于有助于失真 - 扭曲
。 　　FMRIB软件库（FSL）用于分析成像数据57。我们通过现场映射校正和时间（3 dB截止，100 s）和空间滤波（使用全宽度最大最大为5 mm）进行了预处理数据 ，并使用FSL McFlirt纠正了运动 。使用两步过程将功能扫描注册为标准MNI空间：首先，使用（非线性）磁性映射扭曲 - 纠正的BBR进行了受试者的全脑EPI到T1结构图像的注册；其次
，使用仿射转换进行了仿射转换，然后进行非线性注册 ，将受试者的T1结构扫描注册为1 mm标准空间
。在视觉检查后
，我们使用FSL旋律来过滤噪声组件。 　　我们使用FSL壮举进行了第一级分析 。首先，用FSL膜预先怀有数据 ，以解释时间自相关57
。时间衍生物和标准运动参数包括在模型中
，我们使用了双伽马HRF58,59。使用自动离群值 - 降外线和FSL火焰1的群集校正阈值z> 3.1和p计算结果< 0.05. 　　For all whole-brain analyses, all non-constant regressors were normalized to a mean of zero and a standard deviation of 1. In self and partner decisions, we refer to O1 and O2 as the Or and Oi, depending on whether participants were asked to compare their performance or not. 　　In a first GLM (fMRI GLM1), we modelled each RDK as a 2-s constant event time-locked to its onset. This constant captured the player-unspecific variance in the BOLD signal for all random dot motion events. As well as this constant, we specified four parametric regressors that were specific to the performance of each of the players and captured their parametric performance score for this trial (0–6). These regressors also had a duration of 2 s to match the constant’s duration and were time-locked to the onset of the corresponding players’ RDK. Related to participants’ decisions, we constructed six regressors to capture the main activation for decisions, binned by condition and decision number (first or second after the RDK). This meant we had one constant for self decisions that came first (S1) and one constant for self decisions that came second (S2), and did the same for partner decisions and group decisions (termed P1, P2, G1 and G2). These constants had a duration of 2 s, which was the average time participants took to make choices. Furthermore, parametric regressors of interest were time-locked to the same constant effects. For self and partner decisions, we used the following parametric regressors: S performance (indicating performance score associated with self); P performance (indicating performance score associated with partner); Or performance (indicating performance score associated with the relevant opponent); Oi performance (indicating performance score associated with the irrelevant opponent); and bonus. 　　This meant that we used four sets of these parametric regressors, which were each time-locked to the onsets of S1, P1, S2 and P2. The duration of these regressors were also set to 2 s to match the main effects. For group decisions, we used the following set of parametric regressors, each of a duration of 2 s: S performance, P performance, O1 performance, O2 performance and bonus. 　　Using the same logic as for the other trial types, we used two sets of these regressors, separately time-locked to G1 and G2. Note that O1 and O2, the two opponents, were clearly identifiable because the letters O1 and O2 were overlaid over their cues. We coded the fMRI regressors in line with these identities, even though other features of the opponents, such as their position on screen and colour, were randomized across participants (see Extended Data Fig. 1 for details of the visual presentation). Finally, as regressors of no-interest, we modelled button responses as regressors time-locked to all button responses, setting the duration to a standard duration of 0.1 s. 　　In Fig. 1, we present the effects of S performance during S2 and P performance during P2. 　　In the second GLM (fMRI GLM2), we focused on the representation of the basis functions towards the end of the observation phase. As in all analyses related to the basis functions, we tested the parametric effects of the trialwise projections onto the basis functions. We modelled the constant effect of RDKs by time-locking a stick function (duration of 0.1 s) to a time 2 s after the offset of the last RDK in the sequence of four RDKs that were presented at the start of each trial. This time point coincided precisely with the average onsets of the first decision. We time-locked several parametric regressors to the same time point, each with the same standard duration of 0.1 s: b1, b2 b3, S performance, P performance, O1 performance and O2 performance. 　　Again, each parametric regressor was normalized. We also used two parametric regressors related to the position of self and partner in the sequence (S-position and P-position). Each could have a value between 1 and 4 depending on the sequential position of that player. We time-locked these latter two parametric effects to the offset of the last RDK in the sequence when all performances have been presented. 　　We took care to include regressors that account for decision-related activity. We coded the different decision types as three constants, each with a duration of 2 s, as in the previous design: S, P and G decisions. Each constant was accompanied by parametric regressors of the same timing that captured decision related activations: DV, the DV relevant for the current decision, including bonus; DV × C, DV in interaction with choice (engage or avoid on the current trial); choice, a binary variable coded as engage/avoid; DVi, the performance difference of the irrelevant players, coded as own team member versus opponent team member (only defined for self and partner, not group decisions); and DVi × C, DVi in interaction with choice. 　　All interactions were calculated by normalizing both components of the interaction to a mean of zero and a standard deviation of 1, and then multiplying both. Finally, as regressors of no-interest, we modelled button responses as a regressors time-locked to all button responses, setting the duration to a standard duration of 0.1 s. 　　On the contrast level, we combined all basis function projections (b1, b2 and b3) and the S-position regressor, each weighted evenly ([1, 1, 1, 1] contrast; Fig. 3). 　　In this design (fMRI GLM3), we again modelled each random dot-motion kinematogram as a 2 s constant event time-locked to its onset. We combined self and partner decisions to one category (dyadic trials, DY), but split by number of decisions (DY1 for the first decision of both self and partner decisions, and DY2 analogously). The duration of the decision events was set to 2 s, as in the other designs. We time-locked parametric regressors to the DY trials, but separately to DY1 and DY2. These regressors had the same timing parameters as the respective decision constants and they were: 　　We calculated the combined effect across both DY1 and DY2 for the inverted primary and the inverted secondary basis function (see 4 and 10 in above list) using a [1, 1] contrast. We then averaged both of these combined contrasts to estimate the overall effect of inverted primary and secondary basis function combined. Furthermore, we modelled group decisions as a separate constant regressor, collapsed over both the first and second decisions. The duration of this regressor was set to 2 s and we time-locked the following regressors to it: primary basis function; inverted primary basis function; inverted primary basis function in interaction with choice; bonus; and bonus in interaction with choice. 　　For all the above regressors in the GLM, if they are related to the basis functions, they refer to the trialwise projections onto the basis functions. On the contrast level, for DY1 trials (dyadic decisions that came first), we combined the first two basis function projections linearly ([1, 1]; primary + secondary basis function; regressors 1 and 2 in the above list). We also contrasted them with the tertiary basis function projection ([1, 1, −1]; primary + secondary − tertiary function; regressors 1, 2 and 3 in the above list). We also calculated the dyadic decision variable in the reference frame of choice (as chosen versus unchosen). We did this by combining regressors 6, 7 and 9 in the list above over both DY1 and DY2 trials. 　　ROIs had a radius of three voxels and were centred on peak voxels of significant clusters. To guarantee statistical independence, we analysed only those variables that were independent of ROI selection and only epochs that were temporally dissociated from the time period that served for ROI selection. For ROI time-course analyses, we extracted the preprocessed BOLD time courses from each ROI and averaged over all voxels of each volume. The time courses were normalized (per session, as for subsequent analyses), oversampled by a factor of ten (using cubic spline interpolation, as for subsequent analyses) and, in a trialwise manner, aligned at the time point of interest. We then applied a GLM to each time point and computed one beta weight per time point, which resulted in a time course of beta weights for each regressor. We used a leave-one-out procedure to conduct significance tests on the beta-weight time courses. For this, in a predefined time window, we calculated the absolute peak of the time course (defined as the maximal deviation from zero, either positive or negative). We did this for all participants except a left-out participant. We then determined the beta weight of the left-out participant at the time of the peak of the remaining group. In this manner, we determined a beta weight for every participant, which, importantly, was independent of the participant’s own data. We subsequently performed t-tests against zero on these beta weights. 　　We used two time-course designs, both time-locked to the end of the observation phase, which was on average 2 s before the onset of the first decision. All regressors were normalized to a mean of zero and a standard deviation of 1. ROI GLM1 comprised the following regressors: b1, b2, b3, S performance, P performance, O1 performance, O2 performance, S-position (the sequence position of self, which can be can be 1, 2, 3 or 4) and P-position (the same, but for the partner). 　　ROI GLM2 comprised a similar set of regressors: b1, b2, b3, null vector, S-position and P-position. 　　Note that the null vector from ROI GLM2 is the sum of the performance of all players and hence cannot be part of ROI GLM1. For the analysis of the effects, we used an analysis time window of 4–10 s after the observation phase offset. To distinguish those effects from even earlier effects linked to the observation phase itself, we conservatively used an earlier time window of 0–6 s after the offset of the last RDK (only used for S-position; see the main text). The significance of the basis function projections and S-position was tested in ROI GLM1, and the null vector was tested for significance in ROI GLM2. 　　We simulated, analysed and visualized data using Matlab 2021a, Jasp v.0.16 and gramm60. 　　We simulated choices in our experiment to examine the effects of the primary and secondary basis functions on decision making. For all these analyses, primary and secondary basis function projections are inverted (expressed in an agent-centric, social reference frame (see ‘Sorting of basis functions and transformation to choice’). We consider self decisions, but all results hold when simulating partner decisions accordingly. 　　We simulated choices as a linear combination of primary basis projection, secondary basis projection and the non-social bonus (see the DV definitions in the beginning of the Methods section; DVself = S − Or + B). As we have shown analytically above, the correct agent-centric decision variable is given by the linear combination of these three variables, because primary and secondary basis projections in combination result in the performance difference of S and Or, ignoring the two other players. Therefore, simulated choices used a logistic link function and a set of weights for the three predictors (wprim, wsec and wbonus) to estimate choice probabilities, which were then binarized to an engage (1) or avoid (0) decision with a likelihood based on the choice probability. We simulated self decisions for all participants with 200 simulations per participant. We subsequently fitted an agent-centric logistic GLM using S performance, P performance, Or performance, Oi performance and the bonus. Finally, we averaged and plotted beta weights from this GLM and examined the qualitative effects of irrelevant players (P and Or) on self decisions. 　　We simulated choices under two regimes. For both, we chose weight vectors that resulted in beta weights of similar magnitudes to those observed in our behavioural analyses. The first regime was the ‘balanced’ regime, which used identical weights for primary and secondary basis functions, as one would optimally use to analytically derive the agent-centric decision variable (wprim = 1.5, wsec = 1.5 and wbonus = 1.5). The second regime used a relative ‘overweighting’ of the primary over the secondary basis function, as indicated by our previous analyses (wprim = 1.7, wsec = 1.3 and wbonus = 1.5). 　　We used logistic GLMs to capture the weights participants assigned to different pieces of information when making their decisions. We predicted participants’ choices to engage (versus avoid) as a function of a normalized set of regressors (each regressor had a mean of zero and a standard deviation of 1). We applied the GLMs separately to self and partner decisions. The GLM comprised the performance of self (S) and partner (P) as well as the two opponents, separately coded as the relevant opponent (Or; the one whose performance was to be considered in the dyadic comparison) and the irrelevant opponent (Oi; the one whose performance was irrelevant for the dyadic comparison). The GLM also contained the non-social bonus. 　　A time-varying drift diffusion model43 (tDDM) was fitted to the choice outcome (engage or avoid) and reaction time data of our participants. The tDDM expands the standard DDM60,61 by allowing for different onset times of the attributes that influence the evidence accumulation process. Specifically, our tDDM allowed for different onset times between the primary and the secondary basis function (but in agent-centric space). We estimated a total of seven free parameters separately for each participant and experimental condition using the differential evolution algorithm62. The free parameters were the weights of the primary and secondary basis function, the weight of the bonus, the difference in onset times between the primary and the secondary basis function, the decision threshold, the starting-point bias and the non-decision time. The difference in onset times was estimated relative to the onset of the primary basis function. Thus, a positive difference indicates that the secondary basis function entered the evidence accumulation process later than the primary basis function, whereas a negative difference indicates that the secondary basis function entered the evidence accumulation process earlier. The bonus always entered the accumulation process at the same time as the function with the earlier onset. We optimized the tDDM parameters by simulating 3,000 decision outcomes and reaction times per iteration for each unique combination of primary function, secondary function and bonus that the respective participant encountered during the experiment. For any given participant, this could be a subset of all possible combinations, and some combinations could have been encountered repeatedly. The parameters were adapted from iteration to iteration to maximize the likelihood of the empirical data, given the distributions generated from the simulated decisions over a total of 150 iterations. 　　We ran a behavioural experiment online using Prolific (www.prolific.com). The experiment took one hour, and participants were paid £9 for taking part. The ethics committee of the University of Oxford approved the study and all participants provided informed consent (MSD reference number: R70000/RE001). The experiment was programmed using jspsych63 and the random-dot-motion toolbox64. As inclusion criteria, we used the age range of 18–40, and fluent English speakers were recruited in the United States and the United Kingdom. As in the fMRI study, participants first performed a behavioural pre-experiment described as a performance assessment. This comprised, in quick succession, random dot-motion stimuli of varying coherence and took in total about 3 min. Participants were informed that the pre-experiment was relevant for the next part of the study, when they were shown samples of their performance in a group decision-making experiment. After the pre-experiment, the instructions for the decision-making experiment followed. This part, again, was modelled on the fMRI study. After the instructions to the decision-making experiment, participants passed a comprehension check that asked three questions about the task rules. The participants went on to do the experiment only if they responded correctly to all three questions. Otherwise, the experiment was aborted and participants were given a small amount for their time investment (about 5–10 min at this point). After the decision-making experiment, participants filled in some questionnaires unrelated to the purpose of this study. The study was conducted over a time period of three weeks. Data for all versions of the experiment were acquired in parallel. For participants who completed the study multiple times, we only considered their initial participation and discarded subsequent data sets. 　　Of the 805 data sets collected, we excluded participants who: took longer than 2 h to complete the experiment; took longer than 30 s to respond to decision trials in more than 10% of trials; and showed a choice repetition bias in the initial performance assessment or the decision-making part of the study. A choice repetition bias was defined as picking the same choice (left or right button) in more than 85% of trials. This led to the exclusion of 11 participants overall. The final sample comprised 795 participants. 　　After starting the experiment, participants entered the performance assessment stage, which they were told was important for the second, main part of the study. Participants estimated the motion direction of an RDK stimulus and responded with left/right buttons to indicate the corresponding direction. The performance assessment comprised 120 RDK trials, lasting in total about 3 min. The motion coherences were set at 0.512 for 20% of the trials and 0.032 for 80% of the trials, with 0.512 being a higher coherence and therefore an easier decision. Each RDK stimulus was presented for a maximum duration of 1 s, requiring participants to make their decisions within that time frame. If they took longer, they would see a ‘Missed!’ message on the screen and the trial would be marked as incorrect. The performance assessment consisted of two sub-parts. In the first sub-part, participants received feedback on their decisions (yellow circle for correct or red cross for incorrect). Following that, the task continued without any feedback. The reason for this was to prevent participants from becoming fully aware of their performance levels before the main experiment, when they would be exposed to similar stimuli. 　　We modelled the behavioural group decision-making experiment closely on the fMRI study. The behavioural experiment comprised 108 trials. As in the fMRI experiment, each trial consisted of an observation phase and two subsequent decisions (a total of 216 decisions). The only modifications made served to shorten and simplify the task slightly, to adjust it to the time frame and complexity of large-scale online studies. We used no temporal jitters between the observation phase and the first decision phase, and no temporal jitters between the first and the second decision phase of each trial. Furthermore, to slightly reduce the difficulty of the task, we extended the time that a performance cue was shown during the observation phase from 200 ms to 300 ms, with 100 ms delay between cues. Otherwise, the trial timeline was the same as in the fMRI study. The non-social bonus that was symbolized by yellow and red coins during the decision phase in the fMRI experiment was now symbolized by different colours of the arrow that indicated the players to be compared. A positive bonus was indicated by a yellow arrow, and a negative bonus was indicated by a red arrow. This simple colour-coding scheme was possible because we used only two magnitudes of the bonus in the behavioural study: −0.5 and 0.5. 　　We used four versions of the experimental schedule, arranged in a 2 × 2 between-subjects design; the two schedules comprised self, partner and group decisions (the group condition) and two schedules comprised only self and partner decisions (the no-group condition). A schedule was defined by the assignment of performance scores to players for each trial during the observation phase, and by the assignment of the bonus and decision type to each decision in the study. The comparison of participants’ choice behaviour between group and no-group conditions was the focus of this study. The group condition comprised 72 group decisions, 72 self decisions and 72 partner decisions. In half of the self decisions, participants compared their own scores with those of O1 (36 decisions), and in the other half, with O2 (36 decisions). This meant that O1 and O2 were the relevant opponent for the self equally often. The same was true in partner decisions, with O1 and O2 being the relevant opponent equally often. The schedules used in the no-group condition were generated by replacing group decisions with self and partner decisions in equal number (keeping the bonus for all decisions the same). This resulted in 108 self decisions and 108 partner decisions in total. Again, the relevant opponent for each decision type was O1 and O2 equally often. Note that we analysed only self and partner decisions that were identical across conditions (matched decisions). We discarded self and partner decisions in the no-group schedule that were replacements of the group decisions, because these decisions had no direct correspondence across conditions. This resulted in 72 matched self decisions and 72 matched partner decisions. In this way we were able to compare identical decisions in the two conditions, but the identical decisions took place in the context of group decisions in the group condition but not in the no-group condition. 　　Although the schedule defined precisely which performance score was presented for which player on which trial, it did not specify the order in which the players were shown. To determine this, and to avoid any possibility that idiosyncrasies of the player order confounded our results, we generated 1,000 shuffled player-order sequences. Each sequence presented each possible player order equally often. With four players, 4 × 3 × 2 × 1 = 24 different player orders are possible. We used those for 4 × 24 = 96 trials. For the final 12 trials (the experiment comprised 108 trials), the player orders were randomly selected for each of the 1,000 player sequences. Then, for each participant performing the behavioural experiment, one player order was selected randomly out of the 1,000. 　　Overall, we used four experimental schedules. For both group and no-group conditions, we used two schedules that differed only in the precise assignment of scores to players that were shown during the observation phase (schedule 1 and schedule 2). The behavioural differences between these schedules were not of interest for the study’s research question. The two versions were used only to assess the stability of our experimental effects across numerical differences in the information that was to be remembered. For the same schedule version, group and no-group conditions differed only in the presence or absence of the group decisions. Therefore, we made sure to acquire a similar number of participants for each schedule version for both group and no-group conditions. This ensured an equal number of participants in the conditions that we meant to compare in our study as follows: schedule 1, 192 participants in the no-group condition and 190 in the group condition; and schedule 2, 207 participants in the no-group condition and 206 in the group condition. 　　We analysed the behavioural data using Matlab 2021a and Jasp v.0.16. We fitted a logistic GLM to the choice data that we had also used for the fMRI sample. All regressors were normalized (mean of 0, standard deviation of 1) and predicted the choice to engage (1) or avoid (0), that is, whether one’s own team member was judged to be the better performer. As in the fMRI data set, we included S performance, P performance, Or performance, Oi performance and the bonus in the regression. Because the experiment, for timing reasons, comprised fewer trials per participant, we used ridge regression65,66 to estimate the regressors’ beta weights (the effect sizes). Ridge regression penalizes large beta weights according to a regularization coefficient λ and thereby prevents overfitting and improves generalization. This is appropriate for cases such as ours in which there are many regressors and comparatively few trials. We applied the regression model to all sessions using Matlab lassoglm (setting α to a very small value) in the following way. First, we determined an appropriate regularization coefficient λ. To do so, we repeatedly fitted the GLM to each individual dataset while varying λ between zero and 10−3 to 10−1 (log-spaced). During each fit, we used a three-fold cross-validation approach to determine the overall model deviance for each λ for all datasets combined. We repeated this procedure twice. Finally, we selected the λ that resulted in the lowest overall model deviance. This is the λ with the best cross-validated model fit, which was then used to run the ridge GLM of interest. Importantly, the same best-fitting λ was used for all participants, irrespective of condition, to enable fair statistical comparisons of beta weights within and across conditions. 　　We calculated the decision relevance of each player over an experimental schedule in the following way. If the player was irrelevant for a decision (for example, the partner in self decisions), their relevance score was zero. In dyadic trials, both relevant players’ relevance scores were set to 0.5 (that is, self and relevant opponent in self decisions). In group decisions, each player’s relevance score was 0.25 (self, partner, O1 and O2 contribute equally). We determined the relevance scores for all players for all decisions in an experimental schedule, added them up and divided by the number of trials. 　　There were 36 participants. One participant did not complete the scanning session and two participants could not perform the experiment owing to problems with the button box. One participant moved extensively in the MRI scanner and during melodic preprocessing57, and we discovered that very few fMRI components were noise free. These four participants were removed from the sample. The final sample contained 32 participants (age range 19–39 years, 22 female). Participants received £70 for taking part in in the experiment and received extra earnings that were allocated according to their task performance, mirroring the social fMRI experiment. The ethics committee of the University of Oxford approved the study and all participants provided informed consent (MSD reference number: R60547/RE001). 　　As in the main social fMRI experiment, participants performed a behavioural pre-experiment before entering the MRI scanner. However, the framing of the pre-experiment was very different from that of the social fMRI study. Instead of framing the task as a social decision- making experiment, we framed it as a motor task. Participants were told that the experiment was about learning and remembering motor sequences, in particular, sequences of finger taps. To this end, participants performed ‘tap training’ as pre-experiment preparation. They were shown sequences of finger taps and were asked to repeat these sequences. Four buttons were used in the pre-experiment, assigned to the index and middle fingers of the left and right hands. The screen showed the outlines of two hands with the four fingers highlighted (Fig. 5 and Extended Data Fig. 11). During the tap training, one finger at a time was highlighted and participants pressed the corresponding buttons. Fingers were highlighted repeatedly, and participants were asked to press the corresponding buttons until the sequence ended. Incorrect button presses and long response times were counted as error trials and led to the sequence being repeated until it was completed without error. The pre-experiment comprised 15 trials. Participants performed the pre-experiment for approximately 15 min. 　　The pre-experiment helped create the cover story that the study was about motor sequences. However, the pre-experiment was designed to have clear analogies to the observation phase of the social fMRI experiment, which presented sequences of successful (indicated by yellow coins) and erroneous (indicated by red Xs) performance scores. The motor pre-experiment similarly comprised yellow coins to indicate that a button should be pressed and a red X to indicate that a button press should be omitted. The resulting sequence of finger taps in the control fMRI experiment resembled the sequence of four players’ performance scores in the social task. In our social experiment, performance scores for four players had been shown in sequence, but now, the required number of presses for four fingers were shown in a sequence. There were always six yellow/red cues shown per finger (indicating either an executed button press or button press omission), just as six performance cues had been shown per player in our previous social experiment. Finally, in the same way that self and partner were one team, and O1 and O2 were another team in the social experiment, the four fingers naturally grouped together as the two fingers of the left hand and the two fingers of the right hand, so the two hands corresponded to the two teams in the main control fMRI experiment. Just as participants had compared performance scores across players in the social experiment, participants of the control fMRI experiment completed an fMRI experiment, in which they compared the number of finger taps between the fingers of the two hands. Participants never made decisions between fingers from the same hand, just as they had not made comparisons of players from the same team in the social task. 　　The behavioural pre-experiment that took place before scanning and the control fMRI experiment were programmed in Matlab using Psychtoolbox-3 (ref. 55; http://psychtoolbox.org) and in Psychopy (https://www.psychopy.org/). 　　The main experiment was designed to closely match the rationale and the statistics of the social fMRI experiment. The difference between the experiments comprised the framing of the task as a motor experiment versus a social experiment. 　　In the same way that there was continuity between the pre-experiment and the main experiment in the social study, there was a clear relationship between the pre-experiment and the main experiment here too. In both, participants were shown a display outlining their hands, highlighting the left middle (LM) and the left index finger (LI), as well as the right index (RI) and the right middle finger (RM). In the main control fMRI experiment, the hands were placed on the left and right sides of a button box. As in the pre-experiment, participants observed sequences of yellow and red cues indicating executed finger taps and finger-tap omissions. Their task was to remember the number of taps per finger (the number of yellow coin symbols per finger, ranging from 0 to 6) to make good decisions in the second part of the trial. However, importantly, participants did not concurrently press the highlighted buttons. They were purely observing them in the same way as they were observing the performance scores in the social fMRI study. After the observation phase, participants made decisions about the observed information (the number of presses per finger). These decisions were framed as decisions between the two hands (mimicking the two teams from the social fMRI experiment). We arbitrarily mapped the identities of the players from the social task on the control fMRI experiment. We identified LM as motor–self, LI as motor–partner, RI as motor–opponent 1 and RM as motor–opponent 2. This mapping was consequential, because we utilized exactly the same experimental schedules as we had used for the social experiment for the control fMRI experiment. Therefore, 33% of decisions that were previously self decisions were now LM/motor–self decisions comparing the number of button presses between LM and one of the ‘opponent fingers’ RI or RM (both in equal number); 33% of decisions were partner decisions comparing LI/motor–partner with either RI or RM (both in equal number). The remaining 33% of group decisions were now decisions that asked participants to compare the overall number of button presses for the left hand with the overall number of button presses for the right hand. In all decision types, decisions in favour of the left or right hand were to be made by a press using the thumb of the congruent hand. As in the social fMRI experiment, every decision comprised a bonus that had a value of −1.5, −0.5, +0.5 or +1.5. The timing of all trial events was precisely the same as for the social fMRI experiment. We also used the same pay-off scheme as for the social version, meaning that decisions in favour of the left hand led to win or loss of points accumulated, and decisions in favour of the right hand led to no change in overall points accumulated during the experiment. Although this pay-off scheme may have seemed arbitrary in the context of the control fMRI experiment, it ensured that the behavioural and neural results could be compared across the two experimental versions. 　　As in the social fMRI study, this experiment comprised 144 trials; 288 decisions were made, which were distributed evenly between motor–self, motor–partner and both-hands/group decisions. Crucially, we used the same experimental schedules that we had created for the social fMRI experiment. As described above, the four players were mapped onto the fingers. This equivalence meant that precisely the same scores seen for the players in the social experiment were now seen for the corresponding fingers of the motor study. The scores were shown in precisely the same temporal position during the observation phase of the trial, in a manner corresponding exactly to the social version of the experiment on every single trial. And the same logic applied to the decision types (including the size of the bonus) that were precisely matched with the same choice being correct and the same pay-off being at stake for corresponding trials of the two experiments. Moreover, using identical schedules also streamlined the timings across both experiments. The control fMRI experiment therefore used identical timings to the social fMRI experiment for the observation phase, the decision phases and all temporal jitters. In short, from a numerical perspective, the experimental design, as well as the requirements for solving decisions in both experiments, were identical. The experiments differed only in their framing as a social experiment versus a motor sequence task. 　　All behavioural and neural analysis of the motor study closely resembled the analyses run for the original social fMRI study. Behaviourally, we analysed the percentage of correct motor–self and motor–partner decisions, as well as the median reaction types in motor–self and motor–partner decisions. We also calculated the same logistic GLM models for motor–self and motor–partner decisions predicting engage/avoid decisions as a function of the performance scores for motor–self, motor–partner, motor–Or, motor–Oi and the bonus. 　　We acquired neuroimaging data using the same acquisition protocol and implemented an identical preprocessing pipeline and parameters for the whole-brain analyses (see above for details). The fMRI whole-brain designs included the same set of regressors with identical timings to the social fMRI study (fMRI GLM1 and fMRI GLM2), ensuring that main and control task GLMs comprised the same degrees of freedom. We calculated one extra contrast for fMRI GLM2, which was the mean of all basis functions (b1, b2 and b3 weighted by a [1, 1, 1] vector). We set up a new GLM (fMRI GLM4), which was identical to fMRI GLM2, except for one aspect: we replaced the parametric effects of motor–S, motor–P, motor–O1 and motor–O2 with the mean of these three parameters, which corresponded to the null vector. This mirrors to the way in which we tested the null vector in the social fMRI study, which was the purpose of this new GLM. 　　Masks for ROI analyses had a radius of three voxels (the same radius as in the original social fMRI experiment) and were centred on peak voxels of significant clusters. To guarantee statistical independence, we analysed only variables that were independent of ROI selection and only epochs that were temporally dissociated from the time period that served for ROI selection. Within ROIs, we extracted contrast of parameter image (COPE) values from the whole-brain design to assess significance57,67. In this way, we isolated the effects that correspond to S performance in self decisions and P performance in partner decisions (for both analysing only the second decision in a trial), as displayed in Fig. 1 for the social study (fMRI GLM1). This is how we assessed the neural effects of motor–S and motor–P. For fMRI GLM2, we extracted the COPEs for the three basis function projections as well as the contrast relating to their mean (see above). For fMRI GLM4, we extracted the null vector. Furthermore, we used pre-threshold masking to assess the whole-brain significance of the mean effect of b1, b2 and b3 combined. The mask was centred on the pgACC peak from the social fMRI study (MNI = (−8, 42, 14)) and had a radius of 20 mm. We used a threshold of z >3.1，p = 0.05家庭校正25,68 。 　　我们在线运行了第二个行为实验（扩展数据图5）。研究和数据获取的程序与第一个在线实验 ，研究2相同
，初始绩效评估是相同的
。适用了相同的排除条件，与与选择重复标准有关的其他行为研究唯一的区别 ，我们将其分别应用于实验的培训和测试阶段（而不是将其应用于整个决策会议）。我们根据我们的排除标准排除了29名参与者
，最终样本的1,022名参与者 。 　　和以前一样，我们对fMRI研究的小组决策实验进行了建模
。我们实施了与其他行为研究相同的时间和复杂性调整。该实验包括96次试验 。与fMRI实验一样 ，每个试验包括一个观察阶段和两个随后的决定（因此有192个决定）
。对于每个审判，随后的决定是一个小组决定
，随后的决定是二元决定（自我或伴侣决定）。这也意味着，总的来说 ，在整个决策实验中
，25％的决策是自我决策，有25％是伴侣决策 ，而50％是小组决策 。每种决策类型的频率与第一个和第二个决策一样频繁
。 　　我们使用了带有四个不同实验时间表的受试者间设计。这些时间表仅在给定试验中呈现玩家的顺序顺序方面有所不同 。在所有四个版本中
，绩效时间表（在给定试验中分配了哪个绩效分数）和决策时间表（在给定试验中的自我/合作伙伴/小组决定）均相同
。因此，我们可以肯定的是 ，整个时间表的决策行为上的任何系统差异都必须是由顺序播放器位置信息引起的。 　　在2（训练）×2（测试）设计中组织了四个实验时间表 。所有时间表均包括64项初始培训试验和32例随后的测试试验。训练和测试试验之间的差异与每个试验中观察阶段的参与者的顺序顺序有关
。对于每个试验
，所有决策和绩效得分均相同。但是，有两种不同的培训时间表：PRE3和PRE4 。对于PRE3 ，在所有训练试验中
，当提出二元决定时，二元决定是在第二个序列和第三个球员之间进行的
。对于PRE4 ，所有二元决定均在第二和第四个球员之间进行。结果，对于所有四个时间表
，在训练阶段，二元决定总是涉及四人序列的第二名 。但是 ，在PRE3中
，第二个球员将始终与第三名玩家进行比较，在Pre4中 ，第二个玩家将与序列的第四个玩家进行比较
。换句话说
，我们更改了在时间表之间以系统的方式呈现玩家的顺序，但是我们将表现分数分配给球员不断。这也意味着 ，在给定的时间表中
，将遵循的二元决定完全取决于在观察阶段显示玩家的顺序 。在训练阶段进行了64次试验之后，测试阶段随后 ，包括32次试验
。测试阶段也有两个时间表：Post3和Post4
，它们遵循与以前相同的逻辑。在所有测试时间表中，该序列的第一个要素与二元决策有关 。至关重要的是 ，第二个相关球员是第三位置（POST3）的球员，或者是第四位置（POST4）的球员
。这些时间表设计意味着相同的球员位置始终与实验长期的二元决策保持相关。然而
， 这对于参与者来说并不容易注意到，因为只有一半的决定是二元决定 ，而另一半是小组决定 。在小组决策中
，所有四个球员总是相关的。如上所述，参与者没有报告对这种操作的认识
。我们在这四个条件中的每个条件中收集了类似数量的参与者：Pre3/Post3有270名参与者；Pre3/Post4有252名参与者；Pre4/Post3有250名参与者；Pre4/Post4有250名参与者。 　　为了估算与顺序位置相关的决策权重 ，我们回归了参与/避免二元试验中的决策到五个预测指标：顺序中的第一
，第二，第三和第四名球员的性能得分以及奖励 。同样 ，我们使用了与其他行为研究相同的脊回归程序（研究2）
。但是
，由于我们对试验较少（测试阶段的每个参与者只有64个决策），因此我们调整了搜索最合适的λ的范围 ，范围为10-3至100。由于与顺序位置相关的得分
，我们使用了自我和伙伴的性能得分（数字在0到6之间） 。我们颠倒了对手的性能得分（即重新编码为6为0 、5为1
、4 as 2、3 as 2 as 3 、2 as 4
、1 as 4 as 5 and 0 as 6），因为性能范围在3左右对称
。 　　有关研究设计的更多信息可在与本文有关的自然投资组合报告摘要中获得。