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| 经济学家日历：莱因哈德·泽尔腾 |
作者： 发布时间：2007-11-25 15:17:31 来源： 点击数：55
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Reinhard Selten
(born October 5, 1930)
Reinhard Selten教授 Reinhard Selten教授是一位卓越的经济学家，现为德国波恩大学（University of Bonn）经济学荣休讲座教授，也是一九九四年诺贝尔经济学奖得主。
Reinhard Selten 教授在一九五七年获德国法兰克福的歌德大学（Johann-Wolfgang-Goethe-University）颁授数学硕士学位，并于一九六一年获德国法兰克福大学 (Frankfurt University) 颁授博士学位。Selten教授在一九六七至六八年间于美国柏克莱加州大学担任了一年讲座教授，并于一九六九年获德国柏林的自由大学（Free University）委任为经济学讲座教授。一九七二年至一九八四年，他出任德国的University of Bielefeld的数理经济研究院讲座教授，其后任德国波恩大学经济学讲座教授。Reinhard Selten教授现为德国波恩大学经济学荣休讲座教授。
Reinhard Selten教授自一九五零年代中期，开始钻研博弈论，并于一九六五年发表了一项重要研究，透过分析对局者所作出的理性和非理性的决定来预测结局。博弈论被形容为冲突与合作的数学式和研究，可广泛应用于经济、政治及生物学等各方面。Selten教授与John Nash和John Harsanyi两位学者因为「在非合作博弈的均衡分析理论方面有开创性的贡献」，于一九九四年同获诺贝尔经济学奖。Selten教授亦曾获美国、中国、欧洲多所著名大学及学术机构颁授多项奖誉及荣誉博士衔，其中包括二零零零年获德国State North-Rhine Westfalia奖。
Reinhard Selten教授热心支持香港中文大学经济学系的发展，并于二零零二年十月访问中文大学，主持伟伦访问教授公开讲座，讲解博弈论。
Reinhard Selten – Autobiography
I was born in Breslau on October 10th, 1930. At that time, Breslau, now called Wroclaw, belonged to Germany and only German was spoken there. After the second world war Breslau became Polish and the original German population was almost completely replaced by a Polish one. I have never visited Wroclaw after the war. Heavy fighting destroyed most of the town in which I grew up and most of the familiar places of my youth look different now.
When I was born my father owned a business called a "reading circle"; folders containing an assortment of magazines were lent to customers for one week, then recollected and lent out again. The older the folder, the lower was the fee. This was a florishing branch of industry. My father had built up his business in spite of the fact that he became blind at young years and had only three years of school education. Already in the mid-thirties he had to sell his firm because of his Jewish origin. Jews were forbidden to run a business connected to the press. My father did not belong to any religous community and my mother was a protestant. Originally my parents intended to let me grow up without any attachment to a particular religion in order to give me the opportunity to decide for myself later in my life. However, under the prevailing political circumstances it seemed to be better to have me baptized as a protestant. The ceremony is one of my early memories. Much later as a young man I left the protestant church and became unattached to any religion again. Unlike several other relatives my father did not become a victim of the holocaust, since he died after a serious illness already in 1942 before the worst of the terror began.
It was not easy for me to live as a half-Jewish boy under the Hitler regime. When I was 14 I had to leave high school and the opportunity to learn a trade was denied to me. The only career open to me was that of an unskilled worker. Fortunately it turned out that this did not matter much since after about half a year my mother, my brothers, my sister, and I left Breslau on one of the last trains before all outbound railway traffic stopped.
My situation as a member of an officially despised minority forced me to pay close attention to political matters very early in my life. Moreover I found myself in opposition to the political views shared by the vast majority of the population. I had to learn to trust my own judgment rather than
official propaganda or public opinion. This was a strong influence on my intellectual development. My continuing interest in politics and public affairs was one of the reasons why I began to be interested in economics in my last high school years.
After we left Breslau we were refugees, first in Saxonia, then in Austria and finally in Hessia. Until schools opened again in 1946 I worked as a farm boy, first in Austria and later in the village in Hessia where we lived. In 1947, we moved to Melsungen, a small town in which I went to high school until 1951. In these years I developed a strong interest in mathematics. When we still lived in the village near Melsungen, I had to walk to school which took about three and a half hours there and back. During these walks I occupied my mind with problems of elementary geometry and algebra. I still like to hike in forested hills and to think while walking.
When I finished high school, it was clear to me that I would study mathematics, even if I also considered economics and psychology. It took me relatively long to reach my master's degree in mathematics. My studies were not sufficiently concentrated on this goal. One of the reasons was that I went to many lectures which had nothing to do with my study of mathematics. However, it later turned out that some of these extracurricular activities became important for my career. I studied mathematics at the university of Frankfurt from 1951 to 1957. Until I completed my "Vordiplom", the intermediate examination which roughly corresponds to the bachelor's degree, I also had to study physics. Originally I considered to take astronomy as a minor for my master's degree and I actually spent much time trying to get some knowledge of this field but now almost everything is forgotten. What finally turned me away from astronomy was that I became more and more involved in game theory and economics. I am grateful to the Natural Science Faculty of Frankfurt University for the decision to permit mathematical economics as a minor for the master's degree in order to enable me to be the first one to take this choice.
My first contact with game theory was a popular article in Fortune Magazine which I read in my last high school year. I was immediately attracted to the subject matter and when I studied mathematics I found the fundamental book by von Neumann and Morgenstern in the library and studied it. Somewhat later I saw the announcement of a student seminar for economists on game theory, headed by Professor Ewald Burger who taught advanced mathematical courses but also mathematics for economists. I participated in the seminar and Ewald Burger gave me the chance to write a master's thesis in cooperative game theory. He was a man of extraordinary mathematical erudition and an excellent teacher. I owe much to his guidance and to his patient advise.
My master's thesis and later my Ph.D. thesis had the aim of axiomatizing a value for e-person games in extensive form. This work made me familiar with the extensive form, in a time when very little work on extensive games was done. This enabled me to see the perfectness problem earlier than others and to write the contributions for which I am now honored by the prize in memory of Alfred Nobel.
After I had received my master's degree in 1957, I was hired by Professor Heinz Sauermann, an economist at the University of Frankfurt am Main, who employed me for ten years in various assistant positions. It was my task to do research funded by Deutsche Forschungsgemeinschaft, the German counterpart of the National Science Foundation. At first I was supposed to apply decision theory to the theory of the firm, but soon I became involved in economic laboratory experimentation. Fortunately the referees of Sauermann's research proposals approved of this new research direction. This made it possible to finance a small group of young people doing experimental research. Sauermann had about 15 assistants and only two to four of them were involved in experiments. I became something like a foreman of this small detachment. Reinhard Tietz, Volker Haselbarth, Otwin Becker, Klaus Schuster and others belonged to it for longer or shorter periods.
Heinz Sauermann was a remarkable man. He was one of the first to propagate Keynesianism in Germany. In spite of a lack of mathematical training he encouraged his students to do work based on formal models. He always had a good feeling for the trends of the field and therefore was very successful in suggesting the right problem areas to those who did research under his supervision. Moreover he was an excellent administrator and scientific organizer, who did much for the propagation of experimental economics. I owe much to him.
In 1959, I married Elisabeth Langreiner, who for all the years since then helped me to become the person I am now. We would have liked to have children but we do not have any. We both belong to the Esperanto movement and this is how we met. The international language Esperanto has still an important influence on our life.
My first publication was a journal article with the title "Ein Oligopolexperiment" (an oligopoly experiment) written together with Heinz Sauermann and published in 1959. When we began to do experimental economics at Frankfurt, such a field had not yet existed. My attempts to learn some psychology while I studied mathematics had made me acquainted to experimental techniques. I had listened to lectures of the gestalt psychologist Edwin Rausch, who was a careful experimenter, and I had participated in psychological experiments as a subject. Therefore it seemed natural to me to try an experimental approach to oligopoly.
In 1961, I received my Ph.D. in mathematics at the University of Frankfurt am Main. Shortly afterwards Oskar Morgenstern made it possible for me to participate in a game theory conference at Princeton. In the late 50s - I do not remember the year - he had given a talk at Frankfurt and my remarks in the subsequent discussion must have impressed him. In the following years he sometimes asked me to meet him when his travels brought him to Frankfurt. He also gave me financial support for staying several weeks longer at Princeton after the game theory conference. My short visit to Princeton was important for my life since it gave me the opportunity to interact with R.J. Aumann and M. Maschler who were members of Morgenstern's research group at that time.
Around 1958, I became aware of H.A. Simon's seminal papers on bounded rationality and was immediately convinced by his arguments. I tried to construct a theory of boundedly rational multigoal decision making. Together with Heinz Sauermann, I worked out an "aspiration adaptation theory of the firm" which was published as a journal article in 1962. After the Princeton conference in 1961, I visited Pittsburgh for two days in order to establish contacts with H.A. Simon and his associates. The problem of bounded rationality has occupied my mind for a long time but unfortunately with less success than I had hoped for. More and more I came to the conclusion that purely speculative approaches like that of our paper of 1962 are of limited value. The structure of boundedly rational economic behavior cannot be invented in the armchair, it must be explored experimentally.
In the early 60's I had run experiments on an oligopoly game with demand inertia. A game theoretical analysis of this model proved to be too difficult but I was able to solve a simplified version. I found a natural equilibrium but the game has many other equilibria. In order to describe the distinguishing features of my solution, I defined subgame perfectness. My paper, Ein Oligopolmodell mit Nachfrageträgheit (An Oligopoly Model with Demand Inertia) was published in 1965. At that time I did not suspect that it often would be quoted, almost exlusively for the definition of subgame perfectness. Very soon it became clear to me that the perfectness problem is not completely solved by this concept. Therefore in a paper published in 1975, I defined a refined notion of perfectness, now often referred to as trembling hand perfectness.
In 1965, I was invited to a game theory workshop at Jerusalem which lasted for three weeks and had only 17 participants, but among them all the important researchers in game theory, with few exceptions. Game theory was still a small field. We had heated discussions about Harsanyi's new theory of games with incomplete information. This was the beginning of my long cooperation with John C. Harsanyi. Not long after the conference I became a member of a group of game theorists hired by the research firm MATHEMATICA to work on projects for the Arms Control and Disarmament Agency. The group often met for several days near Washington D.C.. I cooperated with John C. Harsanyi on bargaining under incomplete information, but I also did other work on models of nuclear deterrence. The group did not produce anything of practical value for the Arms Control and Disarmament Agency, but nevertheless it was very successful because important theoretical advances, e.g. in the analysis of repeated games of incomplete information by Aumann, Maschler, and Stearns were made there.
In Germany the Ph. D. is not yet the last formal requirement for a career as a university teacher. In addition to this, one is expected to work towards a "habilitation". For this purpose one presents a habilitation thesis, often a monography of an area of research. The habilitation is a permission to lecture independently. In my case the habilitation thesis was a monography on multiproduct pricing. In the academic year of 1967/68 I was visiting full professor at the business school of the University of California, Berkeley. I had completed my habilitation thesis shortly before I left to Berkeley and was habilitated when I came back. In 1970 my habilitation thesis was published as a book.
In 1969, I accepted an offer of the Free University of Berlin, where I was a full professor of economics until 1972. My wife and I liked to live in West Berlin. In these years Germany experienced a period of student unrest, which made teaching difficult and sometimes impossible. The student movement was especially strong at the Free University, but this was not the reason why I moved to the University of Bielefeld in 1972. I was attracted by plans to create a big Institute of Mathematical Economics. However, these plans could not be realized since it finally turned out that the money was not available. Eventually a small institute with only three professors was established. I was not unhappy with this solution since I succeeded to convince the appointment committee that all positions should be held by game theorists. The positions were filled by Joachim Rosenmuller, Wulf Albers, and myself. The concentration on game theory gave us a chance to get some international reputation.
My years at the University of Bielefeld were a productive time. My experimental research continued but I mainly worked on game theory and its application to industrial organization and other areas. After John Harsanyi and I had completed our work on bargaining under incomplete information we decided to attack the problem of selecting a unique equilibrium for every game. He twice came to Bielefeld for a year and I often visited Berkeley for short periods of one or two months. It took us about 18 years to construct a reasonable general theory of equilibrium selection in games. In this time we considered many ideas and rejected two fairly well worked out approaches. Our book of 1988 only describes the theory we finally agreed upon.
On my frequent visits to Berkeley I also had a cooperation with Tom Marschak which resulted in a book on multiproduct pricing published in 1974. I also did experimental work on bargaining under incomplete information together with Austin Hoggatt and his younger associates. In the basement of Barrows Hall at the University of California, Berkeley, Austin Hoggatt had built up the first computerized laboratory for experimental economics. There our experiments were run.
In the twelve years I spent at Bielefeld, I began a close cooperation with Werner Guth, who in some sense is one of my students, even if we never held positions at the same university. We worked on applications of the equilibrium selection theory by John Harsanyi and myself, long before it had reached a final form, but we also did research on other problems like wage bargaining in the framework of a business cycle model. Also other people who later became university professors sometimes came to Bielefeld to seek my advise, namely Ulrike Leopold from Graz, Joel Moulen from Lyon, and Eric van Damme from Eindhoven. Ulrike Leopold also worked on the application of equilibrium selection theory and I wrote some papers together with her. Joel Moulen did Ph.D. work on cooperative game theory and became a professor of mathematics at Jaounde, Kameroun. Eric van Damme needed very little advise and is now a well known game theorist.
One of my students, Jon-ren-Chen, a Taiwanese who was my assistent for many years, has never worked on game theory. He does applied econometric research on international trade and development. He was habilitated at Bielefeld and is now a Professor of Economics at Innsbruck. A student of mine, Rolf Stoecker, who was a promising young experimentalist left me after his Ph.D., joined an insurance company and became its chief executive after 5 years. Later something similar happened to me again in Bonn. My assistent Gerald Uhlich who had done important experimental work on coalition bargaining left the university after his Ph.D. and became the second man in a furniture textile factory. Nevertheless I still nourish the hope that some of the students who now work on experimental economics under my guidance will become university teachers.
At the University of Bielefeld, cross fertilization between different fields is favored by the existence of a unique institution, the center for interdisciplinary research. Talks given there brought me into contact with biologists who made me aware of applications of game theory to biology. A young mathematician, Peter Hammerstein, who had a junior position as a statistical advisor in the biology department made me accquainted with the notion of evolutionary stability. From that time on I developed a strong interest in biological game theory. One of my contributions to this field is the investigation of evolutionary stability in extensive games. However, I also wrote other papers in this area, some with Peter Hammerstein and others with Avi Shmida, a botanist at the Hebrew University of Jerusalem, with whom I cooperate on theoretical models of pollination of flowers by bees. Peter Hammerstein is now a well established theoretical biologist. Another student of mine, Franz Weissing, also started a career as a university teacher of biology.
I find it very interesting to cooperate with scientists in different fields who have little mathematical training but much substantial knowledge. My first experience of this kind was my cooperation with the political scientist Amos Perlmutter with whom I developed the scenario bundle method, a systematic way of constructing simple game models of concrete international conflicts. Unfortunately the results of our research have never been formally published. It is the advantage of this kind of interaction that the judgement of the expert on the empirical facts is not yet contaminated by mathematical models. I had a similar experience with Avi Shmida, even if he as a natural scientist is not quite as unmathematical.
I am grateful to Avi Shmida, not only for his scientific cooperation but also for another reason. Before I came into contact with theoretical problems in botany I hardly could distinguish any flower from any other one. However, I felt that I could not really do work on pollination problems without learning at least a little of the art of recognizing wild flowers. Since then I always carry a flower book on my hikes, except in the winter. I enjoy my often frustrated efforts to identify wild flowers. This activity has opened my eyes to the astonishing diversity and the marvelous beauty of flowering plants.
In 1984, I moved to the University of Bonn, where I am a Professor of Economics since then. I liked the interdisciplinary atmosphere at the University of Bielefeld, but I wanted to build up a computerized laboratory for experimental economics and Bonn was willing to offer me much better conditions in this respect. I came back to Bielefeld for the time from October 1, 1987, to September 30, 1988, in order to act as the organizer of a research year on "game theory in the behavioral sciences" at the center for interdisciplinary research. The cooperation of an international group of participants with backgrounds in economics, biology, mathematics, political science, psychology, and philosophy finally resulted in four volumes on "game equilibrium models" published in 1991.
At the University of Bonn my work and that of most of my assistants is concentrated on experimental economics. It is our goal to help to build up a descriptive branch of decision and game theory which takes the limited rationality of human behavior seriously. The financial support of the Deutsche Forschungsgemeinschaft in the framework of the Sonderforschungsbereich (special research unit) 303 enables us to work in this direction.
In 1991, it was discovered that both, I and my wife, suffer from diabetes. Probably we had this disease for some time without knowing it. As as consequence of diabetes my wife lost both legs up to the knee. Therefore she is now bound to the wheelchair. Moreover her eyesight has become very bad. Nevertheless she does many things in the house, even if everything takes much longer than it used to. She cooks and takes care of our three cats and, what is most important, she maintains a cheerful attitude towards life. We have learnt to adjust to our situation.
From Les Prix Nobel. The Nobel Prizes 1994, Editor Tore Frängsmyr, [Nobel Foundation], Stockholm, 1995
This autobiography/biography was written at the time of the award and later published in the book series Les Prix Nobel/Nobel Lectures. The information is sometimes updated with an addendum submitted by the Laureate. To cite this document, always state the source as shown above.
第二十六届获奖者莱茵哈德·泽尔腾——“博弈论”大家
很多非合作均衡问题产生了旨在淘汰“乏味的”纳什均衡的一个研究计划，主要思想是设定严格的条件，不仅要减少可能的均衡的类数，而且还要避免从经济学的角度看不合理的均衡。泽尔腾为此提出了子博弈完美的概念来解决这个问题。 ——1994年瑞典皇家科学院贺辞
莱茵哈德·泽尔腾（Reinhard Selten）
泽尔腾1930年10月10日出生于德国的布莱斯劳。第二次世界大战以后，布莱斯劳划属波兰，改名为弗罗茨瓦夫。
1951年，泽尔腾高中毕业，尽管他曾考虑在大学学习经济学或心理学，但他最后还是决心选择学习数学。泽尔腾考入了法兰克福大学数学系，1957年毕业，获数学硕士学位。
1957年泽尔腾获得了硕士学位后，被法兰克福大学的经济学家海因茨·萨尔曼教授聘为助手。萨尔曼教授是最早在德国倡导凯恩斯主义的经济学家。一开始泽尔腾被安排将决策理论应用于厂商理论研究，但不久，泽尔腾即迷上了经济学的实验。这项工作得到萨尔曼的支持，于是泽尔腾与几个同事一起开始从事经济学的实验研究。尽管萨尔曼没有受过多少数学训练，但他鼓励助手们对经济问题展开模型研究，他对经济学的发展趋势有很好的直观感觉，并对他的助手们的研究提出了很好的指导。
1959年，泽尔腾与萨尔曼合作发表了他的第一篇学术论文《一个有关寡头的实验》。在当时，实验经济学这门学科还不存在。泽尔腾大学期间学习心理学课程时做实验的经验给他做这项研究打下了基础。
1961年，泽尔腾获得法兰克福大学数学博士学位。不久，摩根斯坦邀请他到普林斯顿大学参加博弈论会议，在这次会议上，泽尔腾与哈萨尼首次相遇。会后摩根斯坦资助泽尔腾在普林斯顿做了一段短期访问学者。在此期间，泽尔腾与摩根斯坦研究集体的其他成员如奥曼、马斯库勒等进行了学术交流，这对于泽尔腾的博弈论研究有重要的促进作用。
主要学术贡献
子博弈精炼
1958年前后，泽尔腾了解到西蒙关于有限理性的论文，并试图构造一个有限理性多目标决策模型。泽尔腾到匹茨堡大学做了两年访问研究，与西蒙及其助手进行了交流。1962年，他与萨尔曼发表了一篇论文《改写厂商理论的想法》。对有限理性问题的研究占用了泽尔腾很多的时间，但并没有取得多少进展。泽尔腾越来越强烈地意识到，像他与萨尔曼1962年发表的文章那样的纯理论研究的价值是有限的，要构造有限理性的经济行为理论必须通过实验的方法，而不是闭门造车。
二十世纪六十年代早期，泽尔腾做了寡头博弈的实验。他发现对该实验模型的博弈理论分析太困难了，只能得到比较简单的分析结果。泽尔腾在分析中发现了一个自然均衡，但同时发现这个博弈有许多其他的均衡。为了描述他的发现，泽尔腾定义了子博弈精炼的概念，并于1965年发表了他最著名的博弈论论文《一个具有需求惯性的寡头博弈模型》。泽尔腾当时没有想到他的这篇文章后来会被广泛引用，并成为了子博弈精炼均衡的正式定义，同时成为后来获得诺贝尔经济学奖的主要原因。
1964年，泽尔腾发表了论文《n人博弈的评价》。这是一篇重要的博弈理论论文，是泽尔腾在博弈理论研究中的另一重大贡献。
1965年，泽尔腾应邀参加在以色列举行的国际博弈论工作会议，由于当时博弈论还是一个很小的研究领域，因此参加会议的只有17个人。但其中包括了当时所有重要的博弈理论研究专家。会上，专家们对哈萨尼关于不完全信息博弈理论的研究成果展开了热烈的讨论。从这次会议起，泽尔腾开始了他和哈萨尼长达20多年的合作研究。
在德国，要做大学教师，博士学位不是全部的要求，还得取得一定的资格，这要求写一篇资格论文，常常是关于某一个研究领域的专题文章。泽尔腾1967年写了一篇多产品定价的专题论文，1970年发表。1967～1968年度，泽尔腾到加州大学伯克利分校做访问教授。之后，泽尔腾取得了从教资格，并在柏林自由大学任经济学教授。
在自由大学任教期间，正值德国学生学潮高涨，教学工作遇到很多困难，有时甚至于不能正常教学，而自由大学的学潮又最甚。这时，泽尔腾想建立一个大型的数理经济学研究所，因此于1972年转到比勒菲尔德大学工作。后来由于资金方面的原因，只建立了一个小型的研究机构。泽尔腾成功地说服了拨款委员会，允许该研究机构聘请博弈论专家，一共3个人。
在比勒菲尔德大学，泽尔腾继续他的实验研究，主要从事博弈理论及其在产业组织与其他领域的应用研究，取得了一系列的研究成果。并开始与哈萨尼合作进行博弈均衡选择的研究，合作研究的成果在1988年发表。泽尔腾在到伯克利的经常性访问中，还与马萨克合作，于1974年出版了一本关于多产品定价理论的书。
在比勒菲尔德大学的12年中，泽尔腾还与古斯有密切的合作。他们研究了泽尔腾与哈萨尼博弈均衡选择理论的应用（当时泽尔腾与哈萨尼的博弈均衡选择理论还远没有定型）。同时，他们在经济周期模型的框架中对工资谈判问题进行了研究。在此期间，泽尔腾还指导过一些学生，其中有些已成为世界知名的博弈论专家，如范·登。
在1987年10月1日～1988年9月30日，泽尔腾作为比勒菲尔德大学“行为科学中的博弈论”研究年的组织者，回到比勒菲尔德大学工作了一年。这一年中，他与经济学家、生物学家、数学家、政治学家、心理学家以及哲学家等一起研究讨论，并于1991年出版了四卷本的《博弈均衡模型》。在波恩大学，泽尔腾的研究主要集中于实验经济学研究，目标是建立一个充分考虑人们行为有限理性的决策理论和博弈理论。
次博奕完美点 针对纳什均衡概念的某些不完善的地方，纳什以后的不少研究者试图精化原来的概念，附加条件以便排除纳什均衡点的缺陷。泽尔腾在这方面提出了两个著名的新概念：“次博弈完美均衡点”或简称“次博弈完美点”和“颤抖手完美均衡点”或简称“颤抖手完美点”。
次博弈完美点是泽尔腾１９６５年提出的。他认为在局中人选择应变计划的博弈中，并非所有纳什均衡点都是同样合理的，因为某些均衡要求局中人具有实施“空洞威胁”的能力，即采用事实上无法实施的应变计划，因而这类均衡解失去实际意义。如“若你今天不让我拥有市场的3/4，我将在以后10年内免费出售产品”。他提出次博弈完美点的概念，是要把依赖于这类威胁的均衡点排除在考虑之外，即在原则上排除直观不合理的纳什均衡。在扩展型模式中，其思想表明了先行者利用其先行地位及后行者必然理性地反应的事实，来达到对其最有利的纳什均衡点。求解次博弈完美点的方法是倒推法。次博弈完美点的概念可以推广到动态多时段博弈的情况。
泽尔腾的次博弈完美点概念简单、直观，且与经济学中许多实际情况如寡头市场等相符合。在许多情景中，由于局中人的策略选择会引起一系列的连锁反应，在策略选择时就应对此加以考虑。但次博弈均衡点集合取决于扩展型博弈的细节，不能完全排除所有不直观不合理的纳什均衡点。为弥补不足，泽尔腾（１９７５）提出了“颤抖手完美点”的概念。
“颤抖手完美点”概念的意蕴是：在博弈中每个局中人按纳什均衡点进行策略选择时难免会犯错误，即偶尔会偏离均衡策略（形象地说，可能手会颤抖）。这样局中人应该选择这样的纳什均衡点，即使得自己犯错误时，其他人按照他们的最佳反应策略，仍如同自己未发生错误一样做出同样的策略选择。事实上，这意味着局中人在策略选择时应考虑到自己有可能做出错误选择，从而会力图避免因自己的偶然错误而蒙受其他局中人改变相应策略给自己带来的损失。当然这一概念假定对任一方的颤抖概率都是一样的。其实，在博弈中人们会更小心地避免在损失大的方向上犯错误，这样向不同方向的颤抖概率就会不同。由此麦逊提出了“适当均衡点”的概念，进一步完善了颤抖手均衡点。
在颤抖手均衡点概念中，泽尔腾利用人类行为包含非理性因素（局中人会犯错）这一特点，形成对理性概念的一种新理解。这种方法无疑是博弈理论的一个重大突破。
此外，泽尔腾在把博弈论应用于具体经济分析方面做出了卓越成就，如对非合作博弈中的联盟形成和议价模型等的深入研究。他在把博弈论应用于实验研究和生物学等方面也有突出贡献。总之，泽尔腾在纳什均衡概念的扩展与深化及博弈论在各学科的应用上都做出了突出贡献，与哈萨尼一起推动了博弈论理论体系的丰富与完善。
著作点击
泽尔腾有著作四部，其中经济学方面的有三部：
《价格制定者厂商的一般均衡》（1974）；
《博弈均衡选择的一般理论》（1988，与哈萨尼合作）；
《战略理性模型与决策理论丛书：系列C：博弈论、数学规划及运筹学研究》（1988）。
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