作者:DNKM
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博弈理论的争议
□张五常
《张五常广州讲演录》在本版４月２３日和３０日发表后，引起很大反响。张五常关于博弈理论的批评尤其引起强烈的争议。针对这些争议，张五常写来此文，专投本报。
一个多月前，我在广州中山大学讲了一次话，惹来意想不到的非议！主要原因，是一个学生问及博弈理论（ｔｈｅｏｒｙ ｏｆ ｇａｍｅｓ），我说还看不到这理论对解释现象有什么用处。
那次讲话被整理后（我没有看过）在《２１世纪经济报道》评论版分上下两期发表，后来被转载到北大的网上论坛，跟着的争议风起云涌，骂我的及替我辩护的大约一半一半。
首先要说两件事。第一是我认为学生骂我是很好的现象。几年来我屡次说内地的学生了不起，但私下里每次都受朋友质疑。这次内地的学子反对我的观点，是很明显的进步。这不是我认为他们对，而是他们不管我是什么教授。
第二件事是不幸的。那是在这次争议中，有些学生说我是凭着大名发言，有点浪得虚名也。这不对。我最讨厌大名。我的“大名”是你们学生强加于我的，我哑仔吃黄莲，有苦自知。这里我要郑重声明：任何学生若再说我凭什么大名，就是看我不起。
学术上的行规你们怎可以不知道。你要批评我的学术，找我发表了的学术文章来出气好了。我是不会回应的，但文章既然发表了，你们大可手起刀落——— —不要斩我，要斩就斩我的文章。不要斩他人对我的引述或诠释，翻译的也作不得准，要斩我亲手写出来的才算是英雄好汉（一笑）。
闲话休提，言归正传。说我不懂博弈理论，虽不中亦不远矣！我只是在１９６２年花过几个星期的时间研读Ｊ．ｖｏｎ Ｎｅｕｍａｎｎ与Ｏ．Ｍｏｒｇｅｎｓｔｅｒｎ的名著：《博弈理论与经济行为》。不是我喜欢读，而是在研究院内选修的一科规定要读。其后在有关博弈理论的几个题材上跟了好一段日子，一无所获。这后者是我今天不认同这理论的一个原因。且让我举出四个我“跟”过的例子。
例一是ｄｕｏｐｏｌｙ与ｏｌｉｇｏｐｏｌｙ，即所谓寡头（指三几个卖家）竞争。这是博弈理论的大题目。只几个人竞争，各出其谋，不是博弈是什么？问题是，虽然只有看得到的两三家在生产出售同一物品，但可能有数以千计的在旁观望，见有利可图才加入。博弈的不单是看得到的三几个人，而还有看不到的数以千计。竞争从来不是指看得到的竞争者，而是包括所有可能的竞争者。博弈理论要算多少个？
大约是１９６６年吧，我从赌城拉斯维加斯驾车到旧金山去，路经之地全是沙漠。天大热，摄氏４０多度，汽车没有冷气，口渴之极。车行了很远都四处无人。后来到了一个地方，见有五六人家，其中一家门前挂着可口可乐的招牌。我急忙跑进去，买了一瓶冰冻的可乐，只２５分钱。我想，要是卖者叫价５元一瓶，也是相宜之极，为什么只售２５分？
离开时，我见到有几个邻家的孩子在地上游玩，恍然而悟。我想，要是卖可乐的人把价格提升，这些孩子就会叫父母替他们购置冰箱，大做可口可乐的生意。
例二是Ｈｏｔｅｌｌｉｎｇ ｐａｒａｄｏｘ，也是有名的博弈游戏。这个怪论说，一条很长的路，住宅在两旁平均分布。要开一家超级市场，为了节省顾客的交通费用，当然要开在长路的中间点。要是开两家，为了节省顾客的交通费用，理应一家开在路一方的１／３处，另一家开在另一方的１／３处。但为了抢生意，一家往中移，另一家也往中移，结果是两家都开在长路的中间，增加了顾客的交通费用。
这个两家在长路中间的结论有问题姑且不谈，但若是有三家，同样推理，他们会转来转去，转个不停，搬呀搬的，生意不做也罢。这是博弈游戏了。但我们就是没有见过永远不停地搬迁的行为。
例三是市场的讨价还价。经济学的课本是不容许讨价还价的，但这种行为触目皆是。怎样解释真的是头痛了。１９６３年我开始想，好几次认为得到答案，但还是两年前想到的答案算是满意的。我的答案姑且不论，传统上有些朋友试以ｃｏｒｅ ｔｈｅｏｒｙ 作解释，也有以博弈理论作解释，都没有收获。我自己的解释是一个大秘密，想了３０多年，读者要再等几个月，读完我正在《２１世纪经济报道》连载的《经济解释》才知道。到时你可能不同意，但我可预先告诉你，我的解释不用博弈理论。是的，讨价还价是最常见的博弈行为，要是博弈理论连讨价还价的存在也不能解释，那又怎能自圆其说？
例四是我在１９６９年推出的“卸责”问题了。这是博弈理论卷土重来的导火线。我不认为“卸责”及好些有关或类同的概念，在解释行为上有大作为。我自己的老师及一些朋友不同意这个观点。我曾经几次细说我的立场，不再说了。不同意是很有趣的事，就让大家不同意下去吧。
例子归例子。我不走博弈理论的路，不是因为我认为人是不博弈的。人当然会博弈，但我们要怎样解释人的行为呢？我不走博弈理论的路，是因为我认为在科学方法上这条路走不过。那是维也纳学派传下来的科学方法。可能不对，但那是我所知的而又认为是可取的。这些年来，我自己想来想去，认为验证理论的含意时，在原则上可以观察到的才算是事实，而验证一定要以事实从事。我因此在抽象理论与事实验证的转接中下了多年功夫，满足了自己的好奇心。
博弈理论的困难，是太深奥了。我看不到，或不能肯定，博弈专家所说的事实是事实；看不到，或不能肯定，博弈理论有什么含意可以明确地被事实推翻。
以科学解释现象或行为，我说过了，不是求对，也不是求错，而是求可能被事实推翻。被推翻的可能要很明确，被推翻了就是推翻了的，然后我们把手指打个“十”字，跪下来祷告，希望上苍保佑，事实不会推翻那验证的含意。
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作者:Ah sa 发表时间:2001年6月4日 21:33
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参考资料:
(1)ｄｕｏｐｏｌｙ与ｏｌｉｇｏｐｏｌｙ:
请参考: Any game-theory paper on entry deterrence or Ch.8 of the "Handbook of Industrial Organization Vol. 1".
(2)Ｈｏｔｅｌｌｉｎｇ ｐａｒａｄｏｘ
Cheung's arguement is equivalent to saying, "we should not use demand-supply theory because Cobweb model may not converge to a stable equilibrium" (不要用供求理论,因蜘网模型没有静态均衡)
(3)市场的讨价还价
请参考: Any paper on bargaining theory or Ch.8 "Bargaining and Cooperation in Two Person Games" in "Game THeory" by Myerson.
..................................................
P.S. All these articles were published after １９６２!
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作者:yoyoyo 发表时间:2001年6月13日 15:27
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我想提供我自己的一个真实案例供大家分析。我不抱任何先入为主的立场，只看哪位仁兄能用他主张的方法（博奕论或经济学ABC）解释。
这是一个真实的事情。在中学的时候，我们上体育课打篮球要分组。不是自由组合，也不是老师指定，而以类似猜拳的方式决定。参赛的人围成一圈，同时伸手，可以选择掌心向上或手背向上，这样掌心向上的人同属一组，手背向上的人同属另一组。当然，不一定刚好出掌心或出手背的人是对半分，那就要重新再来，直到人数刚好对半分为止。这听起来好像很难才能碰到一次对半分的情况，但事实是每次分组，大致只要进行几次就能出现对半分的情况。
在猜拳的游戏里，我们知道如果能迟一点出手，看到对方出手的情况才出手，就有博奕论里所说的“后发优势”。所以在猜拳时，两个人都有强烈的动机要迟出手。用我们那里的话说，这叫“弹簧手”。但相方又会严密监察着对方要同时出手，不能“弹簧手”。然而有趣的是，我发现在上述的决定分组的方式中，也有类似于猜拳的成份，但要进行“弹簧手”的作弊却非常容易。那时我们班上有一个同学的篮球技术超人一等，远远高出平均水平，所以这个同学所在的那一组，几乎必然是能胜出的。我那时就想到了这一点，于是就用“弹簧手”的手法，比那个同学出手迟一点点，知道了那同学出掌心还是手背后，我就马上跟着那同学出同样的手。于是，我是十拿九稳能跟那同学一组，也就是总能在胜出的那一组。
我不知道其他同学是否了解我这条“诡计”。因为人很多，别人也不知道我在使“弹簧手”的法子，不像猜拳时是一对一，只需监察一个人就行了。当然，我总是跟那同学分在一组，有可能会被怀疑，但我有时为了避免受怀疑，偶尔也故意不与那同学分在同一组，但只是偶尔而已。即使我自己了解这个方法，但我也无法判断其他同学有否在使同样的方法，所以这条计策相当保险，我整个高中期间打篮球时只要有那同学参与，我就会使用。据我看，没有人发现我在作弊，否则早就揭发我了。
不知道各位经济学上的大虾如何解释这个现实世界的现象？
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作者:Ah sa 发表时间:2001年6月13日 21:27
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Section (I): An Esstential Distinction
In this message, I want to point out an important distinction (区分)
(a) game theory [比拟:optimization (最优化)]
(b) a model using game theory [比拟:a model using optimization]
Notice that game theory ITSELF in (a), just like optimization itself, is just a handy (便于使用的) tool (工具) for modeling, it has NO EXPLANATORY POWER (解释力) at all!
But, when we impose some constraints & test conditions, we can make use of game theory/optimization to construct a model in (b). If this model can derive (取得) testable implications (可验证含义) that fits empirical facts, then we say this model has explainatory power!
I guess many students against game theory fail to understand this distinction.
This is exactly like we use optimization in consumption/production theory.
Optimization itself cannot explain anything, but I guess no one would say consumption & production theory without explanatory power!
Similarly, game theory just gives us a handy framwork(框架) with which we can easily build up a model, derive equilibrium and testable implications.
Is this necessary(必需的)?
Somethimes yes, sometimes no.
Sometimes, when the phenomena is simple enough, we can do it by inituition (直觉) and no game theoretical approach is needed.
Sometimes, when the problem is complicated (复杂), we need game theory to put concepts(概念) into a simple format (格式), so that we can derive implications easily.
We do exactly the same thing in consumer theory. Sometimes, a law of demand is sufficient(足够的). But sometimes, we need to model the whole optimization procedure (程序), so that we can derive implications like how tax rate/price of good 2/income affect demand.
Some think that everything explanable by game theory can be explained by cost.
I tell you, every phenomena in economics ultimatly (最终) come down to cost, taste and initial endowment. Game theory (just like consumer theory, supply-demand model, walrasian general equilibrium model) is just a way to model, ok?!
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学无新旧，学无中西，中国今日实无学之患，而非中学西学偏重之患 -- 王国维
Re:Re:！！！张五常：博弈理论的争议 (yoyoyo)
作者:Ah sa 发表时间:2001年6月13日 21:52
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Section (II) yoyoyo's example
Suppose we want to model the following facts & derive testable implications.
Observations:
(1) 事实是每次分组，大致只要进行几次就能出现对半分的情况。
(2) 要进行“弹簧手”的作弊非常容易
(3) 我整个高中期间打篮球时只要有那同学参与，我就会使用。据我看，没有人发现我在作弊，否则早就揭发我了...我有时为了避免受怀疑，偶尔也故意不与那同学分在同一组
(4) 我总是跟那同学分在一组 [Ah sa: for most of the time, I guess, otherwise contradicting (3)]
How can we explain for these phenomenon? Notice that game theory is just a handy tool, it CANNOT suggest any explaination at all! All possible explanation come from your knowledge & imagination. But game theory helps you to put these intuition (直觉) into a systematic (成体系的) model, and tell you if your intuition actually works.
Now, lets see the observations one by one:
(1') If all players are randomizing (随机) with probability 1/2, and with a large number of players, this can be explained.
(2') If the detection(发觉) of “弹簧手”is more difficult with more players, this is also possible.
(3') You seem to use the following strategy(策略):
- if that excellent(优秀的) player is there, you will follow him most of the time, but sometimes, you don't
- if he's not there, you will not cheat(欺诈)
(4') It seems that you're the only one who cheats. There're many possinle explanations:
- others are idiots
- only you care so much about win or lose
- only you are an expert in cheating ("弹簧手"王)
- only you are an expert in detecing cheating (抓"弹簧手"王)
...
So we can explain these without game theory, no?
The problem is
(i) We don't know if the above explanationsare conflicting(冲突) or not. That is, we want to know if a model contains all these components (组成部分) (1'- 4'), can we have an equilibrium satisfying (1-4)?
(ii) We we're not just interested in modelling the situation, but also TESTING the model. We want the model to derive some testable implications like:
- How (1-4) changes with the number of players?
- How (1-4) changes with the characteristics of players? Say, more or fewer excellent players.
- How (1-4) changes with the reward of the game? Say this is an NBA game with $1000000000 for the winning team.
- How (1-4) changes with the rules of the game? Say the one who detected cheating would be killed.
(Next time, we'll see how to model the game)
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学无新旧，学无中西，中国今日实无学之患，而非中学西学偏重之患 -- 王国维
Re:Re:！！！张五常：博弈理论的争议 (yoyoyo)
作者:zecon 发表时间:2001年6月13日 22:47
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我觉得应该区分经济学中的数学工具与经济理论，
博弈论、最优化理论应算为数学工具，
consumption/production theory，交易成本理论则是经济理论，
数学工具有助于对现象进行抽象、建模，有助于理论体系的构建、演绎。
数学系统本身是抽象的，其含义需要具体理论的解释（这里的解释是指赋予其具体含义）。经济理论可以根据需要使用合适的数学工具，如博弈论、最优化理论、线性代数等。
因此，我非常赞同Ah sa所说的，
“
game theory ITSELF , just like optimization itself, is just a handy (便于使用的) tool (工具) for modeling, it has NO EXPLANATORY POWER (解释力) at all!
game theory is just a handy tool, it CANNOT suggest any explaination at all! All possible explanation come from your knowledge & imagination. But game theory helps you to put these intuition (直觉) into a systematic (成体系的) model, and tell you if your intuition actually works.
”
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zecon
Re:Re:！！！张五常：博弈理论的争议 (yoyoyo)
作者:Ah sa 发表时间:2001年6月13日 23:26
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Re:Re:！！！张五常：博弈理论的争议
作者:bam119 发表时间:2001年6月13日 23:10
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这个同学所在的那一组，几乎必然是能胜出的。我那时就想到了这一点，于是就比那个同学出手迟一点点
你是自利的，于是就选择能实现最大利益的办法。就象我看到一个美女一个恐龙时去找那个美女说话一样（我是先看到那一个是美女然后做的去找她说话的决定，这是不是一样？如果不一样，那么一个门，一次出美女一次出恐龙，几乎必然是是这样，我那时就想到了这一点，于是就在出美女的时候过去和出来的人说话，是不是一样？）
不过我真的不太懂博弈有不有用，因为我真的不知道。但我想打牌就算一个吧，常打和不常打，常和人配对打和和人乱打之类的，请高人指点
Re:Re:！！！张五常：博弈理论的争议
作者:Ah sa 发表时间:2001年6月13日 23:23
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bam119:
In your example, you're the only one who makes decision. Your welfare depends only on your choice, so we can use just simlpe choice theory to explain it.
In yoyoyo's example, your welfare depends not only on your decision, but also on other players' decision. Similarly, other players'welfare depend also on your decision. It's not straightforward why we should have yoyoyo's observation as an equilibrium.
It is exactly this STRATEGIC INTERDEPENDENCE that we cannot use simple choice theory or supply-demand model. In this case, game theory may have a role to play because it is designed to study situation with strategic interdepedence.
Moreover, we're not just modelling your decision, but a set of observations:
(1) 事实是每次分组，大致只要进行几次就能出现对半分的情况。
(2) 要进行“弹簧手”的作弊非常容易
(3) 我整个高中期间打篮球时只要有那同学参与，我就会使用。据我看，没有人发现我在作弊，否则早就揭发我了...我有时为了避免受怀疑，偶尔也故意不与那同学分在同一组
(4) 我总是跟那同学分在一组
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学无新旧，学无中西，中国今日实无学之患，而非中学西学偏重之患 -- 王国维
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学无新旧，学无中西，中国今日实无学之患，而非中学西学偏重之患 -- 王国维
Re:Re:！！！张五常：博弈理论的争议 (yoyoyo)
作者:Ah sa 发表时间:2001年6月13日 23:36
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zecon:
Yes, I think the following distinction is very important
(a) game theory [比拟:optimization (最优化)]
(b) a model using game theory [比拟:a model using optimization]
Some students claim that (industrial organization or trade) models in game theoretical approach have no explanatory power at all. I think they just mix up (a) & (b).
Of course, game theory as a tool in (a), just like calculus, cannot explain the real world. But, by imposing some constraints (especially test conditions), we can derive an economic model in (b) which can potentially explain real world. Similarly, we can use calculus to build up a production model that explain real world, even though calculus itself has no explanatory power.
In situations where there is strategic interdependence between players (that is their welfare depends on other's decision), we cannot use other modelling techniques (individual maximization, supply-demand approach, general equilibrium approach). Game theoretical seems to be the only sensible approach.
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学无新旧，学无中西，中国今日实无学之患，而非中学西学偏重之患 -- 王国维
Re:Re:！！！张五常：博弈理论的争议 (yoyoyo)
作者:zecon 发表时间:2001年6月13日 23:57
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Ah sa，我想问一下，你觉得以下看法有没有问题？
坚持用博弈论分析经济问题的人认为，
在strategic interdependence between players
的情况下，竞争者是有限的，应该用博弈论来建模。
而不用博弈论的人认为现实中潜在的竞争总是存在的，
对别人决策的依赖可以处理为约束条件，
因此坚持用最优化来建模。
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zecon
Re:Re:！！！张五常：博弈理论的争议 (yoyoyo)
作者:Ah sa 发表时间:2001年6月14日 03:07
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"用博弈论" or "不用博弈论"? I think it depends on cases.
It depends on which model can provide implications with "best fit" of data.
If both works, it depends on which one is more simple.
I have no prejudice on this matter.
However, one should notice that:
(1) It is not true that game theory can only model a finite number of players.
Students may have this misconception because they learnt those duopoly model in textbook. That is just a simple model, a starting point.
Actually, there are numerous literature on entry-deterrance which allow potentially infinite number of entrancts. For simplicity, we usually assume the potential competitors are identical. As a result, we can model a game between the existing firms and one representative entrant. (We are not saying there is only one entrant, but saying that a model with one entrant and infinitly many identical entrants give same prediction)
(2) It is not true that game theory does not use optimization (最优化) which is a fundamental postulate in all economic models.
(3) To be honest, in many situations, I'm not exactly sure how we can use constraints to model the issue of "strategic interdependence". For example, in yoyoyo's example, it's not clear in what way we can "对别人决策的依赖处理为约束条件".
(4) Even though we can use use constraint to represent the "strategic interdependent" elements, individual maximization may not imply an equilibrium outcome.
In the case of price taking identical agents, individual has no market power. Agent's action cannot alter the equilibrium outcome. So the equilibrium outcome is just represented by separated individuals' optimization (for example, market demand is just a horizontal summation of individual demand).
When there is strategic interdependence (for example, oligopolies), equilibrium decision is also "interdependent". Notice that, without game theory, we don't even have an appropriate equilibrium concept for this interdependent situation. Now, game theory provides some nice notions of equilibrium (the well known Nash-type equilibria). Depending on information structure, other concepts of equilibrium are also available.
It's not clear to me at all, how we can do this without a game theoretical approach. Maybe zecon can share some of your experience with us.
参阅：http://bbs.efnchina.com/dispbbs.asp?boardID=2178&ID=12953
