Game Changers: Stories of the Revolutionary Minds behind Game Theory

Game Changers: Stories of the Revolutionary Minds behind Game Theory

by Rudolf Taschner


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In this lively history of game theory, a gifted math educator and science writer explains for lay readers the uses and value of this innovative yet easy-to-understand approach to mathematical modeling. Essentially, game theory interprets life as a game with mathematical rules. By following the rules, decisions can be calculated that result in the greatest benefit for all participants.

The author takes the reader from the 17th century through the Cold War to today's age of turbo capitalism. Along the way he introduces such leading contributors as Blaise Pascal in the 17th century, who invented the theory of probability; Ludwig Wittgenstein in the 20th century, who conceived of the world as a play of words; John Nash (the subject of A Beautiful Mind) in the 1950s, who laid the foundation of modern game theory; and today's practitioners who apply the theory to global finance and military strategy.

As the author shows, game theory is more than a type of cost-benefit analysis; ultimately, it is a quest for meaning.

Product Details

ISBN-13: 9781633883734
Publisher: Prometheus Books
Publication date: 10/03/2017
Pages: 237
Sales rank: 1,239,904
Product dimensions: 6.00(w) x 8.90(h) x 0.90(d)

About the Author

Rudolf Taschner is the author of many books on mathematics and its cultural implications, most recently, The Number That Came in from the Cold: When Math Turns into an Adventure. He has been a professor at the Vienna University of Technology (TU) since 1977. Together with his wife and other colleagues, Taschner founded and runs "," a series of events that presents mathematics as a cultural achievement, located in Vienna's Museumsquartier. In 2004, Taschner was elected "Scientist of the Year." In 2011, he was awarded the Prize for People's Education of the City of Vienna.

Read an Excerpt




"This book is a masterpiece!"

Karl Menger positively shines with joy when he hears these words. He was expecting praise, but to have it lavished upon him like this by his teacher Hans Hahn is still a pleasant surprise.

No pupil, with the exception of Kurt Gödel, a curious, maverick character at the Institute, was rated as highly by Hahn as young Menger. People always had to say "young Menger" when referring to him, since his father, "old Menger," had been a professor at the University of Vienna some years before, enjoying fame as the founder of the Austrian School of Economics. If that wasn't enough, father and son both had what sounded like the same name, the only difference being the first letter — the archaic C for the father, and the modern K for the son.

In actual fact, old Menger had hoped that his son would follow in his footsteps. He himself came from the furthest reaches of the Habsburg Empire — Neu-Sandez in Galicia, a town known for its Chassidic community and Rabbi Chaim Halberstam, who taught there until his death in 1876. The son of a well-to-do family of civil servants — his father, Anton, was a lawyer and his mother, Caroline, was the daughter of a prosperous Bohemian merchant — Carl Menger came into the world in 1840. It was a small and placid world. Since Empress Maria Theresia had unwillingly received Galicia in 1772 in exchange for wealthy and much-coveted Silesia — "She wept, but she accepted," as her victorious archrival, the Prussian King Frederick, mockingly put it — the Habsburgs had been posting doctors, lawyers, teachers, and civil servants to this dreamy land. This was what they did with all of their provinces, a custom that, while not exactly giving the regions freedom, let alone independence, did bestow on them a certain prosperity, security, and progress.

For young Carl Menger, this world was much too circumscribed. He studied law in Prague and the imperial capital Vienna, where he then settled down as a journalist. He wrote feature articles, first for the Lemberger Zeitung — Lemberg (now known as Lviv) was the Galician capital — and later for the Wiener Zeitung. He was fond of writing novels and comedies for serialization, occasional works that he produced while following his true interest, the study of law and political economics. He enjoyed the acquaintance of Count Richard von Belcredi, the minister of state at the time, who familiarized him with economic issues. This enabled Carl Menger to enrich the Wiener Zeitung with his market analysis — the start of his deep interest in the laws of economics.

There was one paradox of economic theory that occupied the young lawyer and economic journalist in the months after gaining his doctorate: the paradox of value, also known as the diamond-water paradox. Nobody can survive without water. This makes it a highly valuable commodity. Very few people truly need diamonds. This makes them intrinsically almost worthless. And yet people pay horrendous sums of money for diamonds and almost nothing for water.

Adam Smith, the eighteenth-century founder of political economics, thought he could solve this paradox by differentiating between "value in use" and "value in exchange." The value in use of water is very high, since everybody needs it. Its value in exchange, on the other hand, is very low. In contrast, the value in exchange of diamonds is very high, hence the high prices paid, although their value in use is low. This rudimentary explanation is not particularly satisfactory, however, since it sheds no light on why there is a difference in the value in exchange.

Even before Adam Smith, the Scottish banker John Law had stated, "Water is of great use, yet of little value; because the quantity of water is much greater than the demand for it. Diamonds are of little use, yet of great value, because the demand for diamonds is much greater than the quantity of them." With this statement, he may well have found the pivotal point that might help to solve the paradox.

By way of explaining the diamond-water paradox, Carl Menger comes up with the idea of a farmer who owns five sacks of wheat. The farmer considers the first sack of wheat as indispensable for life, since he uses it to bake his bread, and so he will not die of hunger. With the wheat in the second sack, which is still valuable for him, he bakes even more bread. This gives him and his family strength. With the wheat in the third sack, which is not particularly valuable, he can feed the animals in his stable. He puts aside the wheat in the fourth sack for sowing the following year. The farmer doesn't actually need the wheat in the fifth sack; he uses it to distil grain schnapps.

If one of the farmer's five sacks were to be stolen, what would he do? If his use of the wheat were always the same, he would divide the wheat in the remaining four sacks into five equal heaps and use each heap for the same purpose as with the original sacks: the first heap for the bread necessary for survival, the second heap for the bread to give him strength, the third heap to feed the animals, the fourth heap for seed, and the fifth for making schnapps. But no farmer would do such a thing — farmers are clever souls, as we know. Rather, he would use the remaining four sacks as described before, omitting only the unnecessary distilling of schnapps.

Indeed, farmers are much too clever to let people steal from them. But the farmer could sell the fifth sack, instead of using it to make schnapps that he and his family might never drink. And what would the farmer consider to be the right price? Carl Menger has the answer: it is the price that the farmer would pay to buy the fifth sack in order to use the wheat to distil the schnapps.

It is not the primary or the secondary use of wheat that determines the price, but rather its marginal use — the use that the farmer makes of an extra sack on top of those he already has in storage. That, says Carl Menger, is why water is so cheap: another liter of water on top of the overflowing abundance already available is viewed as insignificant. Only in the middle of the Sahara can water's worth be measured in diamonds.

The economic theory developed from these simple premises brought Carl Menger fame in the world of economics and politics, and he became one of the most influential figures in the Habsburg monarchy. The University of Vienna named him first an associate professor and later a full professor at the Faculty of Law and Political Science, and he even came to the notice of Emperor Franz Joseph himself, being accorded the honor of spending three months expounding the features of his economic theories to the monarch. He was appointed as the private tutor for the emperor's eighteen-year-old son Rudolf, and the two of them spent two years traveling the length and breadth of Europe. During this time, and in the years that followed until Rudolf's death, it seems that Menger became friends with the highly gifted and sensitive young man, awakening in him an interest in modern, liberal governance. But all the hopes that the Liberals pinned on the young crown prince were dashed with the shots the thirty-year-old Rudolf fired in 1889 to kill his young lover, the seventeen-year-old Baroness Mary Vetsera, and himself.

It was in all probability thanks to his close links to the monarchy that Carl Menger's son Karl, born in Vienna in 1902, was recognized as a legitimate child. For Karl's mother, Hermine Andermann, was Jewish. The Catholic father and the Jewish mother were unable to get married in a land where only marriage ceremonies carried out by the Church or the Synagogue were recognized. The two lived in a union akin to matrimony, in what was then known as a marriage sui juris. Children resulting from such unions were considered to be illegitimate, which signified social ostracism, and Carl Menger took early retirement shortly after the birth of his son in order to protect his family from gossip. He was, therefore, all the more grateful to the monarchy for fulfilling his request to annul his son's status as an illegitimate child.

Menger's departure represented a severe loss for the university, one only exacerbated by the fact that, even though no longer a professor there, he remained in contact with his pupils. Felix Somary, whom Menger appointed as his assistant at the tender age of eighteen during his last years of active service, writes in his memoirs:

At that time, the University of Vienna stood at the forefront of the world's schools of national and political economics. Carl Menger, the leading theoretician, followed by his eminent pupils Böhm-Bawerk and Wieser; Philippovich, the brilliant investigator of productivity; and Inama-Sternegg, the first economic historian, were all there — a unique collaboration of remarkable personalities. The discussions held in the seminars were of an exalted standard, since there were also exceptional talents among the students of my time, such as Schumpeter, Pribram, Mises, Otto Bauer, Lederer and Hilferding. Not one of them would end up staying in Austria.

Despite all his success, one imagines Carl Menger as a melancholic man. His academic achievements were fiercely contested by the German "Historical School of Economics," specifically by its main representative, Gustav Schmoller. The accolades he received, his title of Hofrat (court counsellor) and admittance to the Österreichisches Herrenhaus (Austrian House of Lords) all meant little to him, a man who never made use of his aristocratic title "von Wolfensgrün." In the renunciation of liberalism, he saw the descent into disaster, and he felt vindicated in this view after the outbreak of the First World War and its catastrophic effect on the Habsburg Empire. "The World of Yesterday," as Stefan Zweig had called it, lay irrevocably in ruins, and the dream of a better, prosperous world with a firm economic foundation had vanished forever.

Given such a father, who had, after all, reached the age of sixty-two at the birth of his son and only child, young Karl's childhood was certainly not unencumbered by misery, no matter how financially secure it was. With the commanding image of his father before his eyes, the boy set himself the highest standards from his early years. He attended one of the city's best grammar schools, in the wealthy district of Dobling, between the Vienna Woods and the city center, and felt constantly obliged to get only top marks, ideally the very best in the school. But this was no easy undertaking, since Richard Kuhn and Wolfgang Pauli were fellow pupils of his, just two years above him. The highly gifted Richard Kuhn went on to study chemistry, developed chromatography to the extent that it was suitable for chemical analysis, and was awarded the Nobel Prize for his work on carotenoids and vitamins. Wolfgang Pauli's brilliant mind was even more impressive. He later became known as the "conscience of physics" because his critical eye was always able to separate the wheat from the chaff when it came to all the hypotheses developed by Bohr, Heisenberg, Dirac, and the other notable names of quantum physics. He received the Nobel Prize for his discovery of the Pauli exclusion principle, which helped physicists to find an explanation for the existence of the periodic table of chemical elements.

It is certain that Karl Menger attempted to measure his intellect against Pauli's. Pauli delighted in his intellectual powers. Once, when the physics teacher made a mistake on the blackboard and couldn't find it, despite spending minutes looking for it, Pauli simply grinned devilishly from ear to ear until the teacher finally called out to his prodigy, much to the amusement of the class: "Now Pauli, tell me where the mistake is. I know you've long since found it." After doing his Matura, the Austrian school-leaving exams, Pauli published a scientific article on the general theory of relativity that impressed even Einstein himself. And after just a few terms studying physics in Munich, he wrote a long piece on the theory of relativity for the Encyclopedia of Mathematical Sciences, an article that was published as a work in its own right in 1921, received lavish praise from Einstein, and came to be viewed as a classic.

Karl Menger, Pauli's schoolmate and admirer, was convinced that physics was a subject against which one could measure one's intellectual capabilities, but it was no easy task to persuade his father, who had been living like a recluse since the end of the war in 1918, to share the same opinion. We can almost hear Carl Menger ranting: "First you wanted to go into the theater, which thank God I was able to talk you out of, and now you have turned your mind to this pauper's subject?" Karl had indeed wanted to measure himself not only against Pauli but also against his fellow student Heinrich Schnitzler. Schnitzler's father, Arthur, was one of the leading German-language dramatists of the time, and Heinrich himself had resolved to become an actor and film director, since which his admiring friend Karl had been thinking about writing plays. Drafts of a drama featuring the fabled medieval Pope Joan as its main character lay in the drawer of his desk.

Karl tries to explain: "Forget my theatrical ambitions, Papa, and believe me when I say that studying physics is the right choice. I believe I have a gift for the subject. I am seriously interested in the principles of natural science and, in Goethe's words, in 'what binds the world together at its core.' Besides, it wouldn't be wise to try my hand at economics — I could never compete with you and nor would I want to." His father mumbles something incomprehensible and points his son out of his office. Karl Menger is now free to study physics.

On Währingerstrasse, which runs from the center of Vienna to the outer districts of Währing and Döbling, the large gray building at numbers 38 to 42 housed the institutes of chemistry, physics, and mathematics. Here were the state-of-the-art laboratories, the seminar rooms and lecture halls. The place's best days were behind it, however, since the new republic was devoid of modern industry after the war. Following the collapse of the monarchy, the major industrial centers, above all those in Bohemia and Moravia, had been lost to Czechoslovakia and other successor states. With a capital city of two million people, among them far too many civil servants, and a hinterland still very much dependent on an outdated agricultural system, an impoverished country full of war invalids, widows, and orphans and plagued by the Spanish flu pandemic that was rife at the time could not possibly make any great advances. Major support for scientific research was unthinkable. People were glad enough that the university was able to continue operating after a fashion and could retain its staff despite the meagre salaries. Perhaps Pauli is right to matriculate at Ludwig Maximilian University in Munich, young Menger must have thought to himself as he enters the large dusty mathematics lecture hall on the lower ground floor. But it is still possible to change universities after a couple of semesters. At least for now, he doesn't have the heart to leave his parents, especially his aged father, alone in the desolate surroundings of post-war Vienna.

The general theory of relativity, with which Menger's schoolmate Pauli had already made a name for himself, was expounded up on the fourth floor of the same building by the brilliant professor of physics Hans Thirring, a friend of Einstein and a fellow pacifist. The topic was not included in the beginner's lectures on physics, however, which new students had to attend on the lower floors. In addition, it was compulsory to attend mathematics lectures on the ground floor, these being designed to provide the tools for dealing with theoretical physics. This order was also reflected in the timetable: the mathematics lectures took place at eight and nine o'clock, with the physics lectures following at ten and eleven. And so we can observe young Menger descending the short stairway to the mathematics lecture hall at eight o'clock and joining the handful of people already there.

A triumvirate of professors, all three of international standing, occupied the research and teaching posts at the mathematical institute. As a young man in Gottingen, the bastion of mathematics at the time, Wilhelm Wirtinger, originally from Ybbs, a small town one hundred kilometers west of Vienna, had studied at the feet of the famous scholar Felix Klein and established himself as a gifted and versatile mathematician. His tall, gaunt figure, the neatly trimmed moustache on his oval face, his high forehead, and the dignity with which he carried out his duties all lent him a commanding appearance. And Hofrat Wirtinger — he was the last of the Viennese professors to have received the title of court counsellor — gave lectures of the highest level, extremely demanding and only for students who had carefully prepared for them.


Excerpted from "Game Changers"
by .
Copyright © 2017 Rudolf Taschner.
Excerpted by permission of Prometheus Books.
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Table of Contents

The Players, 9,
Acknowledgments, 11,
Vienna, 2017,
1: Playing with Water and Diamonds, 13,
Vienna, between 1870 and 1928,
2: Playing with Chalk, 25,
Vienna, 1921,
3: Playing with Numbers, 37,
Lyon, 1612,
4: Playing with Chance, 47,
Port Royal des Champs, near Paris, 1655,
5: Playing with Time, 57,
Philadelphia, 1746,
Amsterdam, 1636–1637,
6: Playing with a System, 69,
Paris and Port Royal des Champs, 1659,
St. Petersburg, 1738,
7: Playing with Scholars, 83,
Vienna, between 1921 and 1934,
8: Playing with Two Cards, 95,
Princeton, New Jersey, 1938,
9: Playing with Life and Death, 109,
Budapest, 1908,
Princeton, New Jersey, between 1929 and 1957,
10: Playing with Chickens and Lions, 119,
Princeton, New Jersey 1949,
11: Playing with Prisoners, 131,
Stanford, near Palo Alto, California, 1949,
12: Playing with Profit, 141,
Berkeley, near San Francisco, California, 1980,
13: Playing with the Police, 153,
Vienna, 2002,
14: Playing with Information, 165,
New York City, 1990,
15: Playing with Language,
Cambridge, between 1928 and 1946,
16: Playing with Emotions, 185,
Ios, around 850 BCE,
Barcelona, 2014,
Rome, 1900,
Vienna, 1786,
17: Playing with Existence, 195,
Paris, 1662,
Number Games, 203,
Exercises, 203,
Answers, 210,
Glossary, 217,
Notes, 225,
Index, 229,

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