基于最后通牒博弈案例下的科斯定理完善思考

宋 圭 武

内容提要：本文结合最后通牒案例分析，认为，不管是第一种情况，还是第二种情况，科斯定理正确的表述应是：从社会整体角度看，只有公平或满足一定程度公平的初始资源或产权配置，人们的自愿交易才有可能实现社会整体的资源最优配置；从个人局部决策角度看，人们是按照物质成本加精神成本的总和最小化或物质收益加精神收益的总和最大化来考虑资源配置最优的，并不仅仅是只考虑物质成本最小化或物质收益最大化。

关键词： 科斯定理 最后通牒博弈 公平

作者简介：宋圭武，兰州城市学院特聘教授，原甘肃省委党校二级教授。

罗纳德·哈里·科斯（Ronald H. Coase）,1910年12月29日罗纳德·哈里·科斯出生于伦敦的威尔斯登,2013年9月2日在美国去世。是新制度经济学的鼻祖，美国芝加哥大学教授、芝加哥经济学派代表人物之一，1991年获诺贝尔经济学奖。科斯的代表作是两篇著名的论文。其一是1937年发表的《企业的性质》，该文独辟蹊径地讨论了产业企业存在的原因及其扩展规模的界限问题，科斯创造了“交易成本”（Transaction Costs）这一重要的范畴来予以解释。另一篇著名论文是1960年发表的《社会成本问题》，该文重新研究了交易成本为零时合约行为的特征，批评了庇古关于“外部性”问题的补偿原则（政府干预），并论证了在产权明确的前提下，市场交易即使在出现社会成本（即外部性）的场合也同样有效。科斯发现，一旦假定交易成本为零，而且对产权（指财产使用权，即运行和操作中的财产权利）界定是清晰的，那么法律规范并不影响合约行为的结果，即最优化结果保持不变。换言之，只要交易成本为零，那么无论产权归谁，都可以通过市场自由交易达到资源的最佳配置。芝加哥大学经济学家乔治·斯蒂格勒（1982年诺贝尔经济学奖得主）将科斯的这一思想概括为“在完全竞争条件下，私人成本等于社会成本”，并命名为“科斯定理”。

一、科斯定理及其证明

关于科斯定理存在众多争论。一个是存在不存在科斯定理，或者科斯定理算不算是一个定理，有不同争论。有人认为科斯定理至多只能算“科斯命题”或“科斯猜想”。有人认为科斯定理是一个让人难以理解的理论，如交易成本到底如何定义等。有人认为科斯定理应是一个“伪定理”。另外，若有科斯定理，到底科斯定理的真正含义是什么，也有不同争论。目前，主流的看法是认为科斯定理应当是存在的，并且一些学者将科斯定理主要归结为两种情况：第一，在交易费用为零的情况下，不管权利如何进行初始配置，最终自愿交易都会导致资源配置成本最小化或收益最大化；第二，在交易费用不为零的情况下，不同的权利配置界定会带来不同的资源配置效果，所以产权制度的设置是优化资源配置的基础。有学者将前一种情况称为真空世界的科斯定理，后一种情况为真实世界的科斯定理。

对于第一种情况，科斯是通过一个例子来证明的。例如，一工厂所排放的烟尘对邻近5户居民在室外晾晒的衣服造成了损害。在这个例子中，如果不采取任何措施，每户居民的损失为75美元，共计375美元。可以采取两种办法消除烟尘所造成的损害：在工厂的烟囱上安装过滤网，成本为150美元；或者为居民提供烘干机，成本为每户居民50美元，共计250美元。显然，相对于烟尘所造成的损失，这两种办法都是有效率的；而最有效率的办法是安装过滤网。假定交易成本为零，即居民能够毫无代价地聚集在一起并与工厂谈判，那么，无论权利最初如何界定，都会产生最有效率的结果，即安装过滤网。具体来说，如果权利最初界定为工厂赔偿损失，居民享有清洁空气的权利，那么，工厂将安装过滤网，因为安装过滤网的成本低于赔偿损失和提供烘干机的成本；如果权利最初界定为工厂不赔偿损失，也就是工厂享有排放烟尘的权利，那么，居民将安装过滤网，因为安装过滤网的成本低于烟尘所造成的损失和提供烘干机的成本。因此，如果交易成本为零，无论权利如何初始界定，当事人都可以通过交易实现资源的最优配置。

对于上述科斯定理及其证明过程，有很多学者进行了讨论，认为该定理及其证明主要存在三个方面的问题：一是自愿谈判解的有效性值得怀疑。这里有两个问题：第一，科斯所指的只是一种静态的、双头博弈格局，并且是一种非协同博弈。萨缪尔逊指出，即使是在私人品场合，这类静态的、双头非协同博弈所产生的解也是不确定的。其古诺---纳什解只是一种可能的解，而且一般说来，这种解也不是帕累托最优解。在外在品与公共品领域，即使能自愿交易，又如何能确保其有帕累托有效解呢？萨缪尔逊指出，只有在动态博弈的框架里，双头博弈才可能趋近于帕累托有效。第二，科斯定理所设的经典状态是双头为外在性问题进行自愿谈判，如果参与事端的当事人人数增加了，结果如何？科斯本人认为，即使参与外部性与公共品提供的当事人不止两方，而是由一大批人构成，即使外部性问题是极端糟糕、极端混乱的，只要交易成本为零，谈判仍能达到帕累托有效。但实际情况并非如此。二是科斯定理的成立依赖于一种特定的偏好类型，即偏好是平行的，写成效用函数形式，效用函数便是准线性的。如果两个正在进行关于外在性谈判的当事人中有一人的偏好不是平行的，则最后的均衡便会与产权的初始配置状态有关联。三是用自愿交易的方式解决外在性问题，实质隐含了产权清晰的前提，而产权清晰的过程本身又是会产生社会成本的。

二、最后通牒博弈案例与科斯定理完善

经济学有一个最后通牒博弈案例，可以看成是一种交易费用为零的一种资源配置，但其自愿交易的结果并不符合科斯定理第一种情况。

所谓最后通牒博弈，是指这样一个案例。两人分一笔总数固定的钱，比如100元。方法是：A提出方案，B表决。如果后者同意，则按照方案分，如果后者反对，则两人将一无所。A在提方案时要猜测B的反应，此时自利的A的方案是留给B一点点比如一分，而自己得99.99元。如果B接受了就能得到一分钱，如果拒绝就什么也得不到。英国博弈论专家宾谟做了实验，发现提方案者倾向于50：50，而接受者倾向于，少于30％拒绝，多于30％接收。而且根据美国学者的比较文化研究，不管是在亚马逊流域的原始部落，还是在西方发达国家，上述试验结果都是成立的。但按照科斯定理第一种情况，从个人角度看，除非对方提出分给自己的数额为零，否则，只要对方即使给自己极少的一点，也应当接受为最好，因为有收益总比没有收益强，但实际情况是当对方提出的份额少于30%时，人们倾向于拒绝，这就与科斯定理第一种情况有矛盾。

如何解决这个矛盾，笔者认为，这里应扩展科斯定理中的成本和收益概念。科斯定理中的成本和收益，主要考虑的是物质成本或物质收益，并没有考虑精神成本和精神收益。而在最后通牒博弈中，当事人（不管是决定分配的还是接受分配的）实际考虑的是物质成本、物质收益和精神成本、精神收益的总和，是按照物质成本加精神成本总和最小化和物质收益加精神收益总和最大化来决定资源配置策略的。

对于提案者，一些提方案者倾向于50：50，而不是给自己更多，这里面就有一个精神收益的问题。因为能公平对待对方，可以给自己带来精神收益，让别人对我有尊敬感。反之，则让别人瞧不起自己，让自己有精神损失。

对于接受者，一些人认为当分配给自己的方案少于30％时，倾向于拒绝，这里是考虑到精神成本的问题。由于分配给自己的方案少于30％，一些人会感觉受到不公平对待，必然会有一种精神损失，若这种精神损失大于相应的物质收益，理性的选择必然是拒绝其物质收益，因为若接受，必然导致总收益为负值。

同时，在最后通牒博弈中，我们也看到，从群体角度看，在交易成本为零的情况下，资源配置结果与权利的初始界定（分配比例）是有密切关系的，并不是没有关系，其中权利的初始界定一定要考虑公平因素。若不公平，会引起不同程度的社会对抗。对一个人而言，若当不公平所导致的负效用大于一个人生命的正效用时，这个人甚至可能会用牺牲生命的方式来捍卫公平，在这种情况下，可能会引发个体暴力事件。对社会而言，若当社会不公平导致社会大部分人的总效用为负值时，可能会引发社会骚乱甚至导致社会革命。另外，从最后通牒整个群体博弈过程看，分配方案越公平，会有越多人接受分配方案，最终越有利于实现整个群体物质收益和精神收益总和的最大化。所以，从社会角度看，我们也可以这样认为，对每个个体的初始权利界定越公平，最终自愿交易导致社会资源配置的整体效率会越高。

至于对于科斯定理的第二种情况，权利的初始界定，更应考虑公平问题。因为若交易成本不为零，在以后的市场运行过程中，不公平的初始权利界定，最终会导致社会运行陷入更大范围的不均衡。第一，不公平会进一步导致政治的不均衡。政治可能会被强势群体所左右。第二，不公平会进一步导致财富不均衡。财富不均衡，会导致经济增长乏力。第三，会导致人文精神进一步不均衡。不公平的社会，人文精神也会陷入失衡之中。因为不公平，会让人们充满怨气，时间一久，人们的怨气会化为邪气，邪气泛滥，社会必然堕落。另外，财富不均衡的社会，穷人为了尽快跨越财富鸿沟，各种机会主义行为就会泛滥，投机冒险行为也会增加。

由此，笔者认为，不管是第一种情况，还是第二种情况，科斯定理正确的表述应是：从社会整体角度看，只有公平或满足一定程度公平的初始资源或产权配置，人们的自愿交易才有可能实现社会整体的资源最优配置（注意：这里是指有可能实现最优配置，并非必然是最优配置，因为社会整体的资源配置，还受其它许多因素制约，比如社会大众的理性水平、道德水平、信息不对称等情况，都是重要的制约因素）；从个人局部决策角度看，人们是按照物质成本加精神成本的总和最小化或物质收益加精神收益的总和最大化来考虑资源配置最优的，并不仅仅是只考虑物质成本最小化或物质收益最大化。

另外，由于有些权利是无法有效进行初始界定的，或者无法实现产权明晰，这就需要政府出面解决涉及这些问题的资源配置。政府应在三个方面发挥好职能作用。第一，政府应努力建设公正平等的制度。第二，大力培育公民的公共精神。公共精神，核心是利他精神。对社会发展而言，利他精神的意义是多方面的：一是社会会更容易建立起公正有效的制度；二是会大大降低制度的运转成本；三有利于降低外部性所导致的社会经济损失；四是有利于促进产权保护；五是有利于消解平等与自由的紧张关系，因为没有公共精神，自由会导致不平等，最终导致自由的异化。如何大力培育公民的利他精神，一是要高度重视教育，要从小抓起，从日常小事抓起。另外，利他精神建设离不开社会精英群体的示范引领作用。社会精英人士的精神状态是社会精神状态的风向标，对社会风气具有关键示范引领作用。第三，高效提供社会公共产品。所谓公共产品，是私人产品的对称，是指具有消费或使用上的非竞争性和受益上的非排他性的产品。所谓非竞争性，是指一部分人对某一产品的消费不会影响另一些人对该产品的消费，一些人从这一产品中受益不会影响其他人从这一产品中受益，受益对象之间不存在利益冲突。所谓非排他性，是指产品在消费过程中所产生的利益不能为某个人或某些人所专有，要将一些人排斥在消费过程之外，不让他们享受这一产品的利益是不可能的。对于公共产品或准公共产品，比如国防、治理环境污染、教育、医疗等，由于市场无法清晰界定产权，从而无法有效解决外部性问题，客观需要代表公共利益的政府大力介入。

但政府也不是万能的，也有一个失效的问题，另外，由于政府的产出主要是社会公共利益，而社会公共利益又无法有效衡量。所以，从产出角度建立约束政府的有效制度比较困难。应主要从投入角度完善政府的约束制度。一是要进一步完善物质资源投入制度，包括建立更加公平透明的预算制度和监督制度等。二是要进一步加大精神建设的投入，要大力培育政府人员的公共精神。三是要尽可能选拔富于奉献精神的人员担任政府公职人员。

另外，由于公平与效率是正比例关系，所以，政府在推进改革时一定要把公平放在重要位置。在改革初期，面对不公平状况，改革可优先考虑最弱势群体利益，应使最弱势群体获利最大。

另外，公平的重要性目前也被许多学者的研究所证明。一位美国经济学家艾伯特·里斯根据自己的经济学研究和人生阅历，在一篇纪念文章中写道：“在现实世界，制定工资所涉及的因素似乎与新古典理论中所说的那些因素迥然不同。在现实世界，最重要的决定因素似乎是公平。”①心理学家家丹尼尔·卡尼曼和两名经济学家杰克·尼奇及理查德·塞勒合作研究也证明，公平因素比经济动机更重要。②“社会学家认为，如果某种交易是不公平的，那么处于不利地位的人就会愤怒，由愤怒激发的冲动会迫使交易趋向公平。”③乔治·阿克洛夫和罗伯特·席勒在《动物精神》一书中也指出：“我们认为，对非自愿失业、通货膨胀和总产出之间的关系这类基本的经济现象而言，如果把公平因素考虑在内，就可以容易地给出解释。反之，如果不考虑公平，那么这些现象仍将是不解之谜。”④

三、初始权利如何公平界定

关于公平内涵上的界定，有许多种不同观点。第一种观点认为，优者比劣者多得一些是公平的，强者比弱者多得一些是公平的。古希腊智者卡克利斯就是这样认为的。第二种观点认为，公平就是和谐。这是柏拉图在《理想国》里的观点。第三种观点认为，所谓公平，就是社会财富、荣誉、地位等，应根据每个人付出的贡献进行分配，这样就是公平的。这是亚里士多德的基本观点。亚里士多德认为：政治权利的分配必须以人们对于构成城邦各要素的贡献的大小为依据。第四种观点认为，公平是一个约定。伊壁鸠鲁就认为，公平与正义是人们彼此约定的产物，不存在独立的公平与正义，在任何地点、任何时间，只要有一个防范彼此伤害的相互约定，公平与正义就成立了。对于那些不能相互彼此不伤害的动物而言，就无所谓公平与正义。第五种观点认为，公平就是符合自然法的要求。霍布斯认为，自然法是使人类走出自然状态的条件，也是建立在理性之上的普遍法则。他认为自然法最核心的内容是“已所不欲，勿施于人”，在自然法支配之下，人人都是平等的。遵守自然法就是实现正义、公平、公道。 伏尔泰也认为公平是自然法的基本要求，是普天之下都认为如此，它既不使别人痛苦，也不是以别人的痛苦使自己快乐，实现自然法的要求就是实现了公平。第六种观点认为，公平的分配不是按每个人的贡献，而是应根据影响经济产出的所有要素投入进行分配，这一公平原则也可称为要素公平原则。第七种观点认为，公平就是平均。这种观点在我国封建社会，反映是比较明显的，尤其在农民阶层。如我国历史上每一次农民起义，提出的口号基本上都是要求平均的观点。第八种观点认为，公平就是按需分配。就是按照个人的需要进行分配。这里的问题是，是完全满足个人的需要？还是满足合理需要？还是按照社会必需进行分配？还是首先满足需要最大的人的需要？就是一个需要进一步讨论的问题。第九种观点认为，公平就是最大多数人利益的最大化，这是功利主义的基本观点。第十种观点认为，公平就是给每个人最大的自由，其中最重要的就是机会均等，这是自由主义的典型观点。第十一种观点认为，公平是一个历史范畴，这是马克思主义公平观的基本观点。马克思和恩格斯认为，任何社会的公平都不是抽象的、绝对的和永恒不变的，而是具体的、相对的和历史的，不同的社会存在着不同的公平观念。权力决不能超出社会的经济结构以及经济结构制约的社会文化发展。公平则始终只是现存经济关系的或者反映其保守的方面、或者反映其革命方面的观念化的神圣化的表现。希腊人和罗马人的公平认为奴隶制是公平的；1789年资产者的公平要求废除封建制度，因为据说它不公平。在普鲁士的容克看来，甚至可怜的行政区域条例也是永恒公平的破坏。所以，关于永恒公平的观念不仅因时因地而变，甚至也因人而异。第十二种观点认为，公平就是不嫉妒。有一些西方学者以妒忌与否作为判别公平的依据，弗利就是其代表。他曾对公平作过以下的定义：如果在一分配状态下所有人都不妒忌别人的话，这一分配是公平的。他对妒忌的界定是：一个行为者i认为其效用水平低于像他处于个人j位置相同时能获得的效用水平，个人i就妒忌个人j。第十三种观点认为，公平，就是要让每一个人在福利上尽可能与他人平等或相同，这是福利主义的典型观点。第十四种就是罗尔斯的公平观。罗尔斯认为，作为公平的正义的两个原则是：第一，平等自由的原则，即每一个人对于最广泛的基本自由，与其他人相一致的自由都有着相同的权利。第二，社会的和经济的不平等应当满足两个条件：一是公职和职位向所有人开放，即机会均等的公平原则；二是有利于最小受惠者的最大利益，即差别原则。并且罗尔斯认为，第一优先原则平等的自由优先，自由只有为了自由的缘故而被限制。第二优先原则正义对效率和福利优先，其中机会平等原则优先于差别原则。也就是第一原则优先于第二原则，第二原则中的机会均等原则又优先于差别原则。第十五种观点是德沃金的资源公平观。德沃金认为，公平的分配应当是资源平等，也就是使经济结构中分配给每一个公民的资源尽可能是平等的。其衡量标准就是通过嫉妒检验：一旦分配完成，如果有任何居民宁愿选择别人分到的那一份资源而不要自己的那份，则资源的分配就是不平等的。在资源平等论中，德沃金同时认为，政府和社会应当为个人不能负责的运气负责，但个人应对自己的抱负和选择负责。第十六种观点是能力公平论。这是阿马蒂亚·森的观点。阿马蒂亚·森认为，公平关键是人们有理由珍视的那种生活的可行能力的平等。而可行能力，主要包括免受困苦，诸如饥饿、营养不良、可避免的疾病、过早死亡等基本可行能力，以及能够识字算数、享受政治参与等等的自由。

初始权利如何界定，才算公平？笔者认为，公平应当体现在政治、经济、文化三个领域。在政治领域，所谓公平，就是政治权力的公平分享。由于政治权力分配主要涉及提拔干部和如何用人的问题，问题是如何提拔人如何用人更好，最核心是要体现以德为先、德才兼备原则。在经济层面，笔者认为，所谓公平，主要是经济收益的均衡分配。经济收益主要有两类经济收益：来自先天资源的收益和来自后天劳动的收益。对于来自先天资源的收益，公平的分配原则应是收益平均分享。为什么应是平均分享原则？这里我们可以做一个“无主的黄金”的假设，假设地球及宇宙中的先天资源就是一块丢在路上的没有主人认领的黄金，人类就是过路人。在现实中，若一群过路人遇到了这块无主黄金，这时，过路人如何分配这块黄金才更为公平？显然就是人人平均分配。对于地球和宇宙中的先天资源而言，人类不仅是假设，实质就是过路人，所以，对于这些地球上和宇宙中没有借助人类的力量而生成的资源的收益，对于每一个来到世间的人而言，公平的分配原则就是大家平均分享收益，这也是为大家所共同接受的一种分配方式。对于后天因人类劳动而产生的收益，公平的分配原则应是按劳分配。这里我们假设人类捡到了地球及宇宙这块黄金，这时这群人利用这块黄金开始了劳动，生产了各种产品，但每个人的劳动付出是不一样的，在这种情况下，公平合理的分配原则就是按照每个人的劳动付出支付报酬，也就是按劳分配。但问题是，有些人由于遗传等原因，在劳动能力等方面具有先天的不足，但这种不足不能归结为个人的原因。所以，按劳分配也是有缺陷的。为了弥补先天资源收益平均分配和后天按劳分配的不足，就需要有人道原则做补充，其中完善的社会保障制度就是对这种不足的一种必要补充。在文化领域，公平的体现核心是社会要充满己所不欲、勿施于人等人文精神和理念。（作者：兰州城市学院特聘教授，原中共甘肃省委党校（甘肃行政学院）二级教授）

注释：

①②③④[美]乔治·阿克洛夫、罗伯特·席勒：《动物精神》中信出版集团2016年2月出版，第26页，第29页，第32页，第35页。

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Thoughts on the Improvement of Coase's Theorem Based on the Ultimatum Game Case

Song Guiwu

Abstract: Based on the analysis of the ultimatum game case, this paper holds that, whether it is the first situation or the second one, the correct statement of the Coase Theorem should be: from the perspective of the overall society, only when the initial allocation of resources or property rights is fair or meets a certain degree of fairness, can voluntary transactions among people possibly achieve the optimal allocation of resources for the entire society; from the perspective of individual local decision-making, people consider the optimal allocation of resources based on minimizing the sum of material and mental costs or maximizing the sum of material and mental benefits, rather than merely focusing on minimizing material costs or maximizing material benefits.

Key words: Coase Theorem, Ultimatum Game, Fairness

Author's Profile: Song Guiwu, a specially-appointed professor at Lanzhou City University and former second-level professor at the Gansu Provincial Party School.

Ronald H. Coase was born in Willesden, London on December 29, 1910 and passed away in the United States on September 2, 2013. He is the founder of New Institutional Economics and a representative figure of the Chicago School of Economics at the University of Chicago. He was awarded the Nobel Prize in Economics in 1991. Coase's representative works are two famous papers. One is "The Nature of the Firm" published in 1937, which discussed the reasons for the existence of industrial enterprises and the boundaries of their expansion in a novel way. Coase created the important concept of "transaction costs" to explain this. The other famous paper is "The Problem of Social Cost" published in 1960, which re-examined the characteristics of contractual behavior when transaction costs are zero, criticized Pigou's compensation principle (government intervention) regarding the "externality" problem, and demonstrated that in the case of clear property rights, market transactions are still effective even when social costs (i.e., externalities) occur. Coase discovered that once transaction costs are assumed to be zero and property rights (referring to the right to use property, that is, the rights to operate and manage property) are clearly defined, legal norms do not affect the outcome of contractual behavior, that is, the optimal result remains unchanged. In other words, as long as transaction costs are zero, the best allocation of resources can be achieved through free market transactions regardless of who holds the property rights. George Stigler, an economist at the University of Chicago and the winner of the Nobel Prize in Economics in 1982, summarized Coase's idea as "under perfect competition, private costs equal social costs" and named it "Coase's Theorem".

I. Coase's Theorem and Its Proof

There are numerous debates about Coase's Theorem. One is whether Coase's Theorem exists or not, or whether it can be considered a theorem. Some people believe that Coase's Theorem can at most be called a "Coase proposition" or "Coase conjecture". Some people think that Coase's Theorem is a difficult-to-understand theory, such as how to define transaction costs. Some people believe that Coase's Theorem should be a "pseudo-theorem". Additionally, if Coase's Theorem exists, there are also different debates about its true meaning. Currently, the mainstream view is that Coase's Theorem should exist, and some scholars mainly summarize Coase's Theorem into two situations: First, when transaction costs are zero, no matter how rights are initially allocated, voluntary transactions will eventually lead to the minimization of resource allocation costs or the maximization of benefits; Second, when transaction costs are not zero, different rights allocation definitions will bring different resource allocation effects, so the setting of property rights systems is the basis for optimizing resource allocation. Some scholars refer to the first situation as Coase's Theorem in a vacuum world and the second situation as Coase's Theorem in the real world.

For the first situation, Coase proved it through an example. For instance, a factory's smoke emissions cause damage to the clothes of five neighboring households that are drying outdoors. In this example, if no measures are taken, each household's loss is $75, totaling $375. Two methods can be adopted to eliminate the damage caused by the smoke: installing a filter on the factory's chimney, which costs $150; or providing dryers to the residents, which costs $50 per household, totaling $250. Clearly, both methods are efficient compared to the damage caused by the smoke; and the most efficient method is to install a filter. Assuming transaction costs are zero, that is, the residents can gather together and negotiate with the factory at no cost, then no matter how rights are initially allocated, the most efficient result will be achieved, that is, installing a filter. Specifically, if the rights are initially defined as the factory compensating for the losses and the residents having the right to clean air, then the factory will install filters because the cost of installing filters is lower than the cost of compensating for the losses and providing dryers. If the rights are initially defined as the factory not compensating for the losses, that is, the factory having the right to emit smoke, then the residents will install filters because the cost of installing filters is lower than the losses caused by the smoke and the cost of providing dryers. Therefore, if transaction costs are zero, no matter how the rights are initially defined, the parties can achieve the optimal allocation of resources through transactions.

Many scholars have discussed the Coase Theorem and its proof process, and they believe that there are mainly three problems with the theorem and its proof: First, the effectiveness of voluntary negotiation solutions is questionable. There are two issues here: First, the Coase Theorem only refers to a static, two-party game situation and is a non-cooperative game. Samuelson pointed out that even in the case of private goods, the solutions produced by such static, two-party non-cooperative games are uncertain. Its Cournot-Nash solution is only one possible solution, and generally speaking, this solution is not a Pareto optimal solution. In the field of externalities and public goods, even if voluntary transactions can take place, how can it be ensured that there is a Pareto efficient solution? Samuelson pointed out that only in a dynamic game framework can a two-party game approach Pareto efficiency. Second, the classic state assumed by the Coase Theorem is that two parties voluntarily negotiate about externalities. What if the number of parties involved in the matter increases? Coase himself believed that even if there are not just two parties involved in externalities and public goods provision, but a large number of people, and even if the externalities problem is extremely bad and chaotic, as long as transaction costs are zero, negotiations can still reach Pareto efficiency. But this is not the case in reality. Third, the establishment of the Coase Theorem depends on a specific type of preference, that is, parallel preferences. Written in the form of a utility function, the utility function is quasi-linear. If the preferences of one of the two parties negotiating about externalities are not parallel, then the final equilibrium will be related to the initial allocation of property rights. Fourth, solving the problem of externalities through voluntary transactions implicitly assumes clear property rights, but the process of clarifying property rights itself incurs social costs.

II. The Ultimatum Game Case and the Improvement of the Coase Theorem

Economics has a case of the ultimatum game, which can be regarded as a resource allocation with zero transaction costs, but the result of voluntary transactions does not conform to the first case of the Coase Theorem.

The ultimatum game refers to the following case. Two people divide a fixed amount of money, say 100 yuan. The method is: A proposes a plan, and B votes. If the latter agrees, the money will be divided according to the plan. If the latter refuses, both will get nothing. When A proposes a plan, they have to guess B's reaction. At this time, the self-interested A's plan is to leave B a little bit, such as one cent, and keep 99.99 yuan for themselves. If B accepts, they can get one cent. If they refuse, they will get nothing. British game theory expert Binmore conducted experiments and found that the proposer tends to propose a 50:50 split, while the acceptor tends to accept if the offer is more than 30% and reject if it is less than 30%. Moreover, according to comparative cultural studies by American scholars, this experimental result holds true whether in the primitive tribes of the Amazon Basin or in developed Western countries. But according to the first case of the Coase Theorem, from an individual perspective, unless the other party offers nothing, otherwise, as long as the other party offers even a tiny amount, it should be accepted as the best choice, because having some benefit is better than having none. However, in reality, when the proposed share is less than 30%, people tend to reject it, which contradicts the first case of the Coase Theorem. How to resolve this contradiction? The author believes that the concept of cost and benefit in Coase's theorem should be expanded here. The cost and benefit in Coase's theorem mainly consider material cost or material benefit, without taking into account spiritual cost and spiritual benefit. However, in the ultimatum game, the parties involved (whether the proposer or the responder) actually consider the sum of material cost, material benefit, spiritual cost and spiritual benefit, and decide the resource allocation strategy based on minimizing the total of material cost and spiritual cost and maximizing the total of material benefit and spiritual benefit.

For the proposer, some proposers tend to offer a 50:50 split rather than giving themselves more. This involves a spiritual benefit issue. Because treating the other party fairly can bring spiritual benefit and make others respect them. On the contrary, it will make others look down on them and cause them spiritual loss.

For the responder, some people tend to reject the proposal when the allocation given to them is less than 30%. This is due to the consideration of spiritual cost. When the allocation given to them is less than 30%, some people will feel unfairly treated and will inevitably suffer spiritual loss. If this spiritual loss is greater than the corresponding material benefit, the rational choice is to reject the material benefit, because if they accept it, the total benefit will be negative.

At the same time, in the ultimatum game, we also see that from a group perspective, when transaction costs are zero, the resource allocation result is closely related to the initial definition of rights (allocation ratio), and is not unrelated. The initial definition of rights must take into account the factor of fairness. If it is unfair, it will cause varying degrees of social confrontation. For an individual, if the negative utility caused by unfairness is greater than the positive utility of their life, this person may even sacrifice their life to defend fairness, which may lead to individual violent incidents. For society, if social unfairness causes the total utility of the majority of the population to be negative, it may lead to social unrest or even social revolution. Moreover, from the entire group game process of the ultimatum, the fairer the allocation proposal, the more people will accept it, and ultimately it will be more conducive to maximizing the total sum of material and spiritual benefits of the entire group. Therefore, from a social perspective, we can also say that the fairer the initial rights definition for each individual, the higher the overall efficiency of social resource allocation resulting from voluntary transactions will be.

As for the second situation of Coase's theorem, the initial definition of rights should also consider the issue of fairness. Because if transaction costs are not zero, an unfair initial definition of rights will eventually lead to a larger-scale imbalance in social operation. First, unfairness will further lead to political imbalance. Politics may be dominated by powerful groups. Second, unfairness will further lead to wealth imbalance. Wealth imbalance will lead to sluggish economic growth. Third, it will lead to further imbalance in humanistic spirit. An unfair society will also cause the humanistic spirit to fall into imbalance. Because of unfairness, people will be filled with resentment. Over time, people's resentment will turn into evil, and when evil spreads, society will inevitably decline. In addition, in a society with wealth imbalance, the poor, in order to quickly cross the wealth gap, various opportunistic behaviors will spread, and speculative and risky behaviors will also increase. From this, the author believes that, whether it is the first situation or the second situation, the correct statement of the Coase Theorem should be: From the perspective of the overall society, only an initial allocation of resources or property rights that is fair or meets a certain degree of fairness can people's voluntary transactions possibly achieve the optimal allocation of resources for the overall society (note: here it means that it is possible to achieve the optimal allocation, not necessarily the optimal allocation, because the allocation of resources for the overall society is also constrained by many other factors, such as the rationality level and moral level of the general public, information asymmetry, etc., which are all important constraints). From the perspective of individual local decision-making, people consider the optimal allocation of resources based on the minimization of the sum of material and spiritual costs or the maximization of the sum of material and spiritual benefits, and not merely based on the minimization of material costs or the maximization of material benefits.

In addition, since some rights cannot be effectively defined initially or cannot achieve clear property rights, this requires the government to intervene in the allocation of resources involving these issues. The government should play its role well in three aspects. First, the government should strive to build a fair and equal system. Second, it should vigorously cultivate the public spirit of citizens. The core of public spirit is the spirit of altruism. For social development, the significance of the spirit of altruism is multi-faceted: first, it makes it easier for society to establish fair and effective systems; second, it greatly reduces the operating costs of the system; third, it helps to reduce the economic losses caused by externalities; fourth, it is conducive to promoting property rights protection; fifth, it helps to resolve the tension between equality and freedom, because without public spirit, freedom will lead to inequality and ultimately the alienation of freedom. How to vigorously cultivate the spirit of altruism among citizens? First, great importance should be attached to education, starting from childhood and from daily small matters. In addition, the construction of the spirit of altruism cannot do without the exemplary and leading role of the social elite group. The spiritual state of social elites is the barometer of the social spiritual state and plays a key exemplary and leading role in social customs. Third, provide social public goods efficiently. Public goods are the opposite of private goods, referring to products that have non-competitiveness in consumption or use and non-exclusiveness in benefits. Non-competitiveness means that the consumption of a certain product by some people does not affect the consumption of the same product by others, and some people benefiting from a certain product does not affect others benefiting from it, and there is no conflict of interests among beneficiaries. Non-exclusiveness means that the benefits generated during the consumption process of a product cannot be exclusively owned by an individual or some people, and it is impossible to exclude some people from the consumption process and prevent them from enjoying the benefits of the product. For public goods or quasi-public goods, such as national defense, environmental pollution control, education, and medical care, since the market cannot clearly define property rights, it is impossible to effectively solve the problem of externalities. Therefore, it is objectively necessary for the government, which represents the public interest, to intervene vigorously.

However, the government is not omnipotent and also has a problem of failure. Moreover, since the output of the government is mainly social public interests, and social public interests cannot be effectively measured, it is relatively difficult to establish effective systems to constrain the government from the output perspective. The constraints on the government should mainly be improved from the input perspective. First, the system of material resource input should be further improved, including establishing a more fair and transparent budget system and supervision system, etc. Second, the input of spiritual construction should be further increased, and the public spirit of government personnel should be vigorously cultivated. Third, personnel with a spirit of dedication should be selected as much as possible to serve as government officials.

In addition, since fairness and efficiency are in a positive proportion relationship, the government must place fairness in an important position when promoting reforms. In the early stage of reform, in the face of unfair situations, reforms should give priority to the interests of the most vulnerable groups and ensure that they benefit the most. Moreover, the significance of fairness has also been demonstrated by many scholars' research.An American economist, Albert Rees, based on his economic research and life experiences, wrote in a commemorative article:"In the real world, the factors involved in setting wages seem to be quite different from those mentioned in the neoclassical theory. In the real world, the most important determining factor seems to be fairness." ① Psychologists Daniel Kahneman and two economists Jack Knetsch and Richard Thaler also proved that the factor of fairness is more important than economic motives. ② "Sociologists believe that if a transaction is unfair, then the disadvantaged party will be angry, and the impulse triggered by anger will force the transaction to become fair." ③ George Akerlof and Robert Shiller also pointed out in their book "Animal Spirits" that: "We believe that if the factor of fairness is taken into account, it will be easy to explain the basic economic phenomena such as involuntary unemployment, inflation and total output. On the contrary, if fairness is not considered, these phenomena will remain unsolved mysteries." ④

III. How to Fairly Define Initial Rights

There are many different views on the definition of fairness. The first view holds that it is fair for the superior to get more than the inferior, and for the strong to get more than the weak. This was the view of the ancient Greek philosopher Callicles. The second view holds that fairness is harmony. This was Plato's view in "The Republic". The third view holds that fairness means that social wealth, honor, status, etc. should be distributed according to each person's contribution. This is Aristotle's basic view. Aristotle believed that the distribution of political rights must be based on the size of each person's contribution to the elements that constitute the city-state. The fourth view holds that fairness is an agreement. Epicurus believed that fairness and justice are the products of mutual agreements among people, and there is no independent fairness and justice. As long as there is a mutual agreement to prevent mutual harm at any place and any time, fairness and justice are established. For animals that cannot avoid mutual harm, there is no such thing as fairness and justice. The fifth view holds that fairness is in line with the requirements of natural law. Hobbes believed that natural law is the condition for humans to get out of the state of nature and is a universal law based on reason. He believed that the core content of natural law is "Do not do to others what you do not want others to do to you". Under the rule of natural law, everyone is equal. Adhering to natural law is to achieve justice, fairness and equity. Voltaire also believed that fairness is the basic requirement of natural law, which is recognized by all people in the world. It neither causes others pain nor makes oneself happy at the expense of others' pain. Achieving the requirements of natural law is to achieve fairness. The sixth view holds that fair distribution is not based on each person's contribution, but should be based on the distribution of all factors that affect economic output. This fair principle can also be called the principle of factor fairness. The seventh view holds that fairness is equality. This view was reflected more prominently in China's feudal society, especially among the peasant class. For example, every peasant uprising in Chinese history basically put forward the slogan of equality. The eighth view holds that fairness is distribution according to need. That is, distribution according to each person's need. The question here is whether to fully meet each person's need, or to meet reasonable needs, or to distribute according to social necessity, or to first meet the needs of those with the greatest needs. This is a question that needs further discussion. The ninth view holds that fairness is the maximization of the interests of the greatest number of people. This is the basic view of utilitarianism. The tenth view holds that fairness is giving each person the greatest freedom, with the most important being equal opportunity. This is the typical view of liberalism. The eleventh view holds that fairness is a historical category. This is the basic view of the Marxist concept of fairness. Marx and Engels believed that fairness in any society is not abstract, absolute or unchanging, but concrete, relative and historical. Different societies have different conceptions of fairness. Power must never exceed the economic structure of society and the social and cultural development constrained by it. Fairness is always merely the idealized and sanctified manifestation of the conservative or revolutionary aspects of existing economic relations. The Greeks and Romans regarded slavery as fair; in 1789, the bourgeoisie's fairness demanded the abolition of the feudal system because it was said to be unfair. To the Prussian Junkers, even the poor administrative district regulations were a violation of eternal fairness. Therefore, the concept of eternal fairness not only varies from time to time and place to place, but also from person to person. The twelfth view holds that fairness means not being envious. Some Western scholars use envy as the basis for judging fairness, and Fleur is a representative. He once defined fairness as follows: if no one envies anyone else in a distribution state, then this distribution is fair. His definition of envy is: if an actor i believes that his utility level is lower than what he could obtain if he were in the position of actor j, then actor i envies actor j. The thirteenth view holds that fairness means making everyone's welfare as equal or similar as possible, which is a typical welfareist view. The fourteenth view is Rawls' concept of fairness. Rawls believes that the two principles of justice as fairness are: first, the principle of equal freedom, that is, everyone has the same right to the most extensive basic freedoms consistent with the freedoms of others. Second, social and economic inequalities should meet two conditions: one is that public offices and positions are open to all, that is, the principle of fair equality of opportunity; the other is that they are to the greatest benefit of the least advantaged, that is, the difference principle. And Rawls believes that the first priority principle of equal freedom takes precedence, and freedom can only be restricted for the sake of freedom. The second priority principle of justice takes precedence over efficiency and welfare, among which the principle of fair equality of opportunity takes precedence over the difference principle. That is, the first principle takes precedence over the second principle, and the principle of fair equality of opportunity within the second principle takes precedence over the difference principle. The fifteenth view is Dworkin's resource fairness view. Dworkin believes that fair distribution should be resource equality, that is, the resources allocated to each citizen in the economic structure should be as equal as possible. The measurement standard is the envy test: once the distribution is completed, if any resident would rather choose the resources allocated to others than their own, then the distribution of resources is unequal. In the theory of resource equality, Dworkin also believes that the government and society should be responsible for luck that individuals cannot be responsible for, but individuals should be responsible for their own aspirations and choices. The sixteenth view is the capability fairness view. This is Amartya Sen's view. Amartya Sen believes that the key to fairness is the equality of people's feasible capabilities to live the kind of life they have reason to value. And feasible capabilities mainly include basic capabilities such as freedom from suffering, such as hunger, malnutrition, avoidable diseases, premature death, and capabilities such as being able to read and write, enjoy political participation, etc. How to define initial rights to be considered fair? The author believes that fairness should be reflected in the political, economic and cultural fields. In the political field, fairness means the fair sharing of political power. Since the distribution of political power mainly involves the issue of promoting cadres and how to use people, the key is how to promote and use people better, and the core is to reflect the principle of giving priority to virtue and having both virtue and talent. In the economic field, the author believes that fairness mainly means the balanced distribution of economic benefits. Economic benefits mainly include two types of economic benefits: benefits from innate resources and benefits from acquired labor. For the gains derived from innate resources, the principle of fair distribution should be equal sharing. Why should it be the principle of equal sharing? Here we can make a hypothesis of "ownerless gold", assuming that the innate resources on Earth and in the universe are like a piece of gold left on the road with no owner claiming it, and human beings are passers-by. In reality, if a group of passers-by encounter this ownerless gold, how should they distribute it more fairly? Clearly, it should be shared equally among everyone. For the innate resources on Earth and in the universe, human beings are not just a hypothesis but are actually passers-by. Therefore, for the gains from these resources that were not generated by human efforts, the fair distribution principle for every person who comes into the world is that everyone should share the gains equally. This is also a distribution method that is widely accepted. For the gains produced by human labor after birth, the principle of fair distribution should be distribution according to work. Here we assume that humans picked up the gold of the Earth and the universe, and then started to work with this gold, producing various products. However, the labor input of each person is different. Under such circumstances, the fair and reasonable distribution principle is to pay remuneration according to each person's labor input, that is, distribution according to work. But the problem is that some people have inherent deficiencies in labor capacity due to genetic and other reasons, and such deficiencies cannot be attributed to personal reasons. Therefore, distribution according to work also has its shortcomings. To make up for the deficiencies of equal sharing of gains from innate resources and distribution according to work for gains produced after birth, the principle of humanity needs to be supplemented. Among them, a perfect social security system is a necessary supplement to such deficiencies. In the cultural field, the core of fairness is that society should be filled with humanistic spirits and concepts such as "do not do to others what you do not want others to do to you". (Author: Distinguished Professor of Lanzhou City University, former Second-Class Professor of the Communist Party School of Gansu Province (Gansu Administration College))

Note:

[US] George Akerlof, Robert Shiller: Animal Spirits, published by CITIC Press Group in February 2016, pages 26, 29, 32, 35.

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