赖因哈德·泽尔滕Reinhard Selten

赖因哈德·泽尔滕的父亲Adolf Selten是种族上的犹太人，但没有宗教信仰。泽尔滕的母亲Käthe Luther是新教徒。Adolf Selten没有受过多少教育，只上过三年学。他还年轻时便失明，这使他难以工作养家，但他设法建立了一家兴旺的企业。泽尔滕在[2]中谈到他的父亲：-

我出生时，父亲经营着一家名为“阅读圈”的生意；装有各种杂志的文件夹借给顾客一周，然后收回再借出。文件夹越旧，费用越低。

1933年纳粹党在德国上台后，通过了法律，禁止犹太人从事与新闻业相关的职业，因此Adolf Selten被迫出售了他的生意。阿道夫和凯特决定，鉴于他们的宗教立场，他们会让泽尔滕在没有任何宗教依附的情况下长大，以便他在达到适当年龄时可以自己选择。然而，鉴于纳粹从1933年开始对犹太人采取的行动，他们决定让泽尔滕受洗成为新教徒[2]：-

仪式是我早期的记忆之一。很久以后，作为一个年轻人，我离开了新教教会，再次不依附于任何宗教。

受洗成为新教徒并没有使泽尔滕免于在纳粹德国与犹太父亲一起成长的严重问题。他十一岁时父亲去世[2]：-

与其他几位亲戚不同，我的父亲没有成为大屠杀的受害者，因为他在1942年已经因重病去世，那是在最严重的恐怖开始之前。

由于是半个犹太人，泽尔滕在14岁之后被剥夺了受教育的机会，不得不作为非技术工人就业，但这种情况很短暂，因为第二次世界大战即将结束。当苏联军队逼近被纳粹设防的布雷斯劳市时，德国人开始离开，逃亡始于1944年。1945年5月该市落入俄罗斯人手中前不久，撤离人员的火车停止运行，但泽尔滕与他的母亲、兄弟和姐妹一起，设法乘坐最后几列火车之一逃离了这座城市。这家人在萨克森住了一段时间，然后搬到奥地利，泽尔滕在那里做农场劳工。然后他们搬到奥托·黑塞，住在一个小村庄里，泽尔滕再次做农场工人。1946年，第二次世界大战结束后，德国学校重新开放，泽尔滕得以继续他的教育。1947年，这家人住在梅尔松根，这是黑塞北部的一个小温泉镇，位于卡塞尔以南约20公里处。泽尔滕于1947年至1951年在梅尔松根文理中学学习，此时他对数学产生了兴趣[2]：-

我不得不步行上学，往返大约需要三个半小时。在这些步行途中，我让头脑思考初等几何和代数的问题。

当他完成高中学业时，泽尔滕知道自己想学习数学，但他也有许多其他兴趣，包括经济学和心理学。尽管他当时不可能意识到这一点，但他在学校的最后一年读到《财富》杂志上关于博弈论的一篇文章时，已经朝着他最终的职业迈出了重要的一步。1951年他进入美因河畔法兰克福的约翰-沃尔夫冈-歌德大学时，虽然在攻读数学学位，但出于兴趣选了许多与主修专业无关的课程。当然，博弈论是数学的一部分，他通过在大学图书馆找到的冯·诺伊曼和Morgenstern的Theory of Games and Economic Behaviour继续对这一主题的兴趣。1955年他获得了Vordiplom（大致相当于学士学位）。继续在法兰克福攻读硕士学位时，泽尔滕除了撰写数学学位论文外，还必须提交一个次要科目参加考试。他对博弈论和经济学的兴趣日益增长，这使他询问是否可以把数学经济学而不是天文学作为次要科目。这一请求被允许，他成为第一个选择这一选项的学生。他的关于合作博弈论的硕士论文由Ewald Burger指导。泽尔滕写道[2]：-

他是一个具有非凡数学学识的人，也是一位优秀的教师。我非常感激他的指导和耐心的建议。

1957年，泽尔滕从法兰克福获得数学硕士学位。在接下来的十年里，他在法兰克福大学担任Heinz Sauermann的经济学助理。他在[2]中解释了他所从事的工作：-

我的任务是由德国研究联合会（美国国家科学基金会的德国对应机构）资助进行研究。起初我应该将决策理论应用于企业理论，但很快我就参与了经济学实验室实验。幸运的是，Sauermann研究提案的评审人批准了这一新的研究方向。这使得资助一小群年轻人进行实验研究成为可能。Sauermann大约有15名助理，其中只有两到四名参与实验。我成了这个小分队的类似工头的人。

泽尔滕的众多兴趣之一是国际语言世界语，正是通过世界语他遇到了另一位爱好者Elisabeth Langreiner；他们于1959年结婚。泽尔滕于1961年从法兰克福获得博士学位。此后不久，他接受了Oskar Morgenstern的邀请，参加在普林斯顿举行的博弈论会议，Morgenstern还安排了资金支持，使泽尔滕能够在会议结束后在普林斯顿待几周。他写道[2]：-

我对普林斯顿的短暂访问对我的一生很重要，因为它给了我机会与当时是Morgenstern研究组成员的R J Aumann和M Maschler交流。

在返回德国之前，泽尔滕在匹兹堡逗留了几天，参加博弈论会议之后，以便与Herbert Simon取得联系，后者在有限理性方面的工作对泽尔滕的研究具有重要意义。1965年，他参加了在耶路撒冷的一个小型研讨会，在那里他第一次遇到了弗瑞兹·约翰 C Harsanyi；两人从那时起开始了合作。在1967-68年访问加州大学之后，乔治·伯克利，泽尔滕向法兰克福大学提交了关于多产品定价的Habilitationsschrift，该奖项于1968年颁发。1969年，泽尔滕被任命为柏林自由大学的经济学讲席。他写道[2]：-

我和妻子喜欢住在西柏林。在这些年里，德国经历了学生动乱时期，这使得教学变得困难，有时甚至不可能。学生运动在自由大学尤其强烈，但这不是我在1972年搬到比勒费尔德大学的原因。我被创建大型数学经济学研究所的计划所吸引。然而，这些计划无法实现，因为最终发现资金不可用。

在比勒费尔德大学数学经济学研究所工作十二年后，他搬到了波恩大学的讲席，那里正在建立一个实验经济学实验室。然而，他在1987-88年回到比勒费尔德，主持了一个为期一年的行为科学博弈论研究研讨会。

1965年，他发表了重要著作Ein Oligopolmodell mit Nachfrageträgheit Ⓣ（一个具有需求惯性的寡头垄断模型），关于在预测博弈结果时区分合理和不合理的决策。他出版了书籍：（与约翰 C Harsanyi）A General Theory of Equilibrium Selection in Games（1988）；Models of Strategic Rationality（1988）；和Game Equilibrium Models（1991）。由于他在博弈论方面的工作，泽尔滕与约翰 C Harsanyi和约翰·福布斯·纳什共同获得了1994年诺贝尔经济科学奖：-

……因为他们对非合作博弈理论中均衡的开创性分析。

约翰·福布斯·纳什和泽尔滕各自的贡献如下。约翰·福布斯·纳什将博弈论分为两部分：合作博弈，其中可以达成有约束力的协议；以及非合作博弈，其中不可能达成有约束力的协议。约翰·福布斯·纳什以其非合作博弈的均衡概念做出了重大贡献。它现在被称为约翰·福布斯·纳什均衡。泽尔滕研究了这个概念，他改进了约翰·福布斯·纳什均衡概念，用于分析动态策略互动。泽尔滕还将其改进版的这些概念应用于其他问题，例如分析只有少数卖者时的竞争。在获得诺贝尔奖时，泽尔滕于1994年12月9日发表了他的诺贝尔演讲。他的摘要如下：-

多阶段博弈中各阶段的顺序，通常通过将较早阶段视为涉及更长期决策来加以解释。为了使这一解释精确化，引入了有界多阶段博弈的延迟超级博弈概念。如果博弈进行的长度有一个上界，则多阶段博弈是有界的。延迟超级博弈在许多期中进行。所有阶段的决策同时做出，但直到生效之前有不同的延迟。阶段越早，延迟越长。有界多阶段博弈的子博弈完美均衡在其每一个延迟超级博弈中生成一个子博弈完美均衡。这是本文的第一个主要结论。子博弈完美均衡集是一组子博弈完美均衡，它们不仅在整个博弈中，而且在其每个子博弈中都产生相同的支付。第二个主要结论涉及具有唯一子博弈完美均衡集的多阶段博弈及其在期数有限的意义上有界的延迟超级博弈。如果一个有界多阶段博弈具有唯一的子博弈完美均衡集，那么它的每一个有界延迟超级博弈也是如此。最后，根据所得到的结果，讨论了多阶段博弈模型及其子博弈完美均衡的描述相关性。

获得诺贝尔奖后，他又出版了许多其他著作：Game Theory and Economic Behaviour（1999）；与Michael Schreckenberg合著的Human Behaviour and Traffic Networks（2004）；以及与Daniel Friedman和Alessandra Cassar合著的Economics Lab: An Intensive Course in Experimental Economics（2004）。

除诺贝尔奖外，泽尔滕还获得了许多奖项的荣誉。他于2000年获得Nordrheim Westfalen州奖，2006年获得艺术与科学功勋勋章。他当选为美国艺术与科学院、Rheinisch-Westfalen Akademie der Wissenschaften以及计量经济学会会士。他获得了以下大学的荣誉学位：比勒费尔德大学（1989）、法兰克福大学（1991）、格拉茨大学（1996）、东英吉利大学（1996）、诺里奇大学（1997）、卡尚大学（1998）、因斯布鲁克大学（2000）、香港大学（2003）和奥斯纳布吕克大学（2006）。

Reinhard Selten's father, Adolf Selten, was racially Jewish but had no religious affiliation. Reinhard's mother, Käthe Luther, was a protestant. Adolf Selten had not received much in the way of education, spending only three years at school. When he was still young he went blind making it difficult for him to work to support his family yet he had managed to build up a flourishing business. Reinhard Selten spoke about his father in [2]:-

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.

The coming to power of the Nazi party in Germany in 1933 led to the passing of laws which prevented Jews from holding employment connected to the press, so Adolf Selten was forced to sell his business. Adolf and Käthe had decided that, given their religious positions, they would let Reinhard grow up without any religious attachment so that he could make his own choice when he reached the appropriate age. However given the moves made by the Nazis against the Jews beginning in 1933, they decided that they would have Reinhard baptised as a protestant [2]:-

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.

Being baptised as a protestant did not save Selten from the severe problems of growing up in Nazi Germany with a Jewish father. When he was eleven years old his father died [2]:-

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.

Being half-Jewish, Selten was denied an education beyond the age of 14 and had to take employment as an unskilled worker but this situation was short-lived since World War II was drawing to a close. As Soviet troops approached the city of Breslau, which had been fortified by the Nazis, German people began to leave, the exodus beginning in 1944. Shortly before the city fell to the Russians in May 1945, trains evacuating people stopped running but Selten, along with his mother, brothers and sister, managed to escape the city on one of the last trains. The family lived for a while in Saxony before moving to Austria when Selten worked as a farm labourer. Then they moved to Hesse where they lived in a small village and Selten again worked as a farm worker. In 1946 German schools opened again following the end of World War II and Selten was able to continue his education. In 1947 the family were in Melsungen which is a small spa town in northern Hesse about 20 km south of Kassel. Selten studied at Melsungen Gymnasium from 1947 to 1951 and at this time he became interested in mathematics [2]:-

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.

When he completed high school, Selten knew that he wanted to study mathematics but he also had many other interests including economics and psychology. Although he could not have realised it at the time, he had already made a significant start towards his final career when he read an article on game theory in Fortune Magazine in his final year at school. When he entered the Johann-Wolfgang-Goethe-University in Frankfurt am Main in 1951, although working towards a mathematics degree, he took many courses out of interest which had nothing to do with his main subject. Game theory, of course, was a part of mathematics and he continued his interest in that topic by reading von Neumann and Morgenstern's Theory of Games and Economic Behaviour which he found in the university library. He was awarded his Vordiplom (essentially equivalent to a BA) in 1955. Continuing to work at Frankfurt for a Master's degree, Selten had to present a minor topic for examination in addition to writing a mathematical dissertation. His increasing interest in game theory and economics led to him to ask if he could take mathematical economics as a minor subject instead of astronomy. This was allowed and he became the first student to take this option. For his Master's thesis on cooperative game theory he was advised by Ewald Burger. Selten wrote [2]:-

He was a man of extraordinary mathematical erudition and an excellent teacher. I owe much to his guidance and to his patient advice.

In 1957 Selten was awarded a Master's degree in mathematics from Frankfurt. For the next ten years he worked as an assistant in economics to Heinz Sauermann at Frankfurt University. He explained in [2] the work he undertook:-

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.

One of Selten's many interests was the international language Esperanto and it was through this that he met another enthusiast Elisabeth Langreiner; they married in 1959. Selten was awarded his doctorate from Frankfurt in 1961. Shortly after this he accepted an invitation from Oskar Morgenstern to participate in a game theory conference in Princeton, and Morgenstern also arranged financial support to allow Selten to spend a few weeks at Princeton after the conference ended. He wrote [2]:-

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.

Before returning to Germany, Selten spent a couple of days in Pittsburgh following the game theory conference so that he could make contact with Herbert Simon, who had produced work on bounded rationality that was significant to Selten's research. In 1965 he attended a small workshop in Jerusalem where he met John C Harsanyi for the first time; the two began joint work from this time. After spending the year 1967-68 visiting the University of California, Berkeley, Selten submitted his Habilitationsschrift on multiproduct pricing to Frankfurt University, the award being made in 1968. In 1969 Selten was appointed to a chair of economics at the Free University in Berlin. He wrote [2]:-

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.

After twelve years at the Institute for Mathematical Economics of the University of Bielefeld he moved to a chair at the University of Bonn where an experimental economics laboratory was being set up. However, he spent the year 1987-88 back at Bielefeld running a year-long research workshop on game theory in the behavioural sciences.

In 1965 he published important work Ein Oligopolmodell mit Nachfrageträgheit Ⓣ on distinguishing between reasonable and unreasonable decisions in predicting the outcome of games. He published the books: (with John C Harsanyi) A General Theory of Equilibrium Selection in Games (1988); Models of Strategic Rationality (1988); and Game Equilibrium Models (1991). For his work in game theory Selten was, jointly with John C Harsanyi and John Nash, awarded the 1994 Nobel Prize in Economic Science:-

... for their pioneering analysis of equilibria in the theory of non-cooperative games.

The respective contributions of Nash and Selten are as follows. Nash divided game theory into two parts, cooperative games, in which binding agreements can be made, and non-cooperative games, where binding agreements are not possible. Nash made a significant contribution with his equilibrium concept for non-cooperative games. It is now called the Nash equilibrium. Selten worked on this concept and he refined the Nash equilibrium concept for analysing dynamic strategic interaction. Selten has also applied his refined version of these concepts to other problems such as analysing competition when there are only a small number of sellers. On receiving the Nobel prize, Selten gave his Nobel Lecture on 9 December 1994. His abstract is as follows:-

The order of stages in a multistage game is often interpreted by looking at earlier stages as involving more long term decisions. For the purpose of making this interpretation precise, the notion of a delay supergame of a bounded multistage game is introduced. A multistage game is bounded if the length of play has an upper bound. A delay supergame is played over many periods. Decisions on all stages are made simultaneously, but with different delays until they become effective. The earlier the stage the longer the delay. A subgame perfect equilibrium of a bounded multistage game generates a subgame perfect equilibrium in every one of its delay supergames. This is the first main conclusion of the paper. A subgame perfect equilibrium set is a set of subgame perfect equilibria all of which yield the same payoffs, not only in the game as a whole, but also in each of its subgames. The second main conclusion concerns multistage games with a unique subgame perfect equilibrium set and their delay supergames which are bounded in the sense that the number of periods is finite. If a bounded multistage game has a unique subgame perfect equilibrium set, then the same is true for every one of its bounded delay supergames. Finally the descriptive relevance of multistage game models and their subgame perfect equilibria is discussed in the light of the results obtained.

After the award of the Nobel prize he published a number of other books: Game Theory and Economic Behaviour (1999); (with Michael Schreckenberg) Human Behaviour and Traffic Networks (2004); and (with Daniel Friedman and Alessandra Cassar) Economics Lab: An Intensive Course in Experimental Economics (2004).

Selten has been honoured by many awards in addition to the Nobel Prize. He received the Nordrheim Westfalen State Prize in 2000 and the Order of Merit Arts and Sciences in 2006. He was elected to the American Academy of Arts and Sciences, to the Rheinisch-Westfalen Akademie der Wissenschaften, and to a fellowship of the Econometric Society. He received honorary degrees from Bielefeld University (1989), Frankfurt University (1991), Graz University (1996), University of East Anglia (1996), Norwich University (1997), Cachan University (1998), Innsbruck University (2000), Hong Kong University (2003) and Osnabrück University (2006).