Game Theorists

"There is no shortage of disputes."

"Game theory, however, deals only with the way in which ultrasmart, all knowing people should behave in competitive situations, and has little to say to Mr. X as he confronts the morass of his problem."

"Ideas are incestuous."

"That was a documentary!"

"I've always been with the one who rebels against false values. My heroes now are Ralph Nader and Daniel Ellsberg."

"Chelsea Manning is again acting heroically in the name of press freedom, and it’s a travesty that she has been sent back to jail for refusing to testify to a grand jury. An investigation into WikiLeaks for publishing is a grave threat to all journalists’ rights, and Chelsea is doing us all a service for fighting it. She has already been tortured, spent years in jail, and has suffered more than enough. She should be released immediately."

"The question really arises is it a republic if you can keep it, question have we kept it? And the answer is no! No we have not kept it. Since 2001 we have in effect an elected monarchy. And ah, meaning a country which Nixon's view 'when a president does it, it is legal'. The president says it's not illegal. That is the attitude long after Nixon of John Yoo, who was the advisor to George W. Bush, of David Addington, Bush Cheney's legal advisor. Essentially there are no limits on presidential power except those which he chooses to put on himself. Obama following on, has in effect decriminalized torture which is as illegal and criminal as anything can be under international law and domestic law, a number of domestic laws and international laws, which we have ratified to investigate, and follow-up if there is any credible charge. Obama has chosen not to investigate or indict any higher up for that process of torture."

"EVERY attack now made on WikiLeaks and Julian Assange was made against me and the release of the Pentagon Papers at the time."

"I took that opportunity to tell him something that, er, I had long thought of telling somebody that was about to enter the world of really high secrecy. And I said, 'Henry, you're about to get a lot of clearance higher than top secret that you did not know existed. That's going to have a sequence of effects on you. First, a great exhilaration that you're getting all this amazing information that you didn't know even existed. And the next phase is you'll feel like a fool for not having known about any of this. but that won't last long. Fairly soon, you'll come to think that everyone else is foolish. What would this expert be telling me if he knew what I knew? So in the end, you stop listening to them."

"The American public was lied to [about the Vietnam War] month by month by each of these five administrations [Truman, Eisenhower, Kennedy, Johnson, Nixon]. It's a tribute to the American public that their leaders perceived that they had to be lied to. It's no tribute to us that it was so easy to fool the public."

"We weren't on the wrong side. We are the wrong side."

"Natural selection is the only workable explanation for the beautiful and compelling illusion of 'design' that pervades every living body and every organ. Knowledge of evolution may not be strictly useful in everyday commerce. You can live some sort of life and die without ever hearing the name of Darwin. But if, before you die, you want to understand why you lived in the first place, Darwinism is the one subject that you must study."

"It is in the nature of science that once a position becomes orthodox it should be subjected to criticism.... It does not follow that, because a position is orthodox, it is wrong."

"Тhе сепtгаl роіпt геmаіпs that Darwin provided a theory which predicts that organisms should have parts adapted to ensure their survival and . This has led to the suggestion that life should be defined by the possession of those properties which are needed to ensure evolution by natural selection. That is, entities with the properties of multiplication, variation, and are alive, and entities lacking one or more of those properties are not."

"It is an occupational risk of biologists to claim, towards the end of their careers, that the problems which they have not solved are insoluble."

"John Maynard Smith, an engineer by training, knows much about his biology secondhand. He seldom deals with live organisms. He computes and he reads. I suspect that it's very hard for him to have insight into any group of organisms when he does not deal with them directly. Biologists, especially, need direct sensory communication with the live beings they study and about which they write."

"Game theory concepts were first explicitly applied in evolutionary biology by Lewontin (1961). His approach, however, was to picture a species as playing a game against nature, and to seek strategies which minimised the probability of extinction. A similar line has been taken by Slobodkin & Rapoport (1974). In contrast, here we picture members of a population as playing games against each other, and consider the population dynamics and equilibria which can arise."

"Darwin's theory of evolution by natural selection is the only workable explanation that has ever been proposed for the remarkable fact of our own existence, indeed the existence of all life wherever it may turn up in the universe."

"The theory of games was first formalised by Von Neumann & Morgenstern (1953) in reference to human economic behaviour. Since that time, the theory has undergone extensive development... Sensibly enough, a central assumption of classical game theory is that the players will behave rationally, and according to some criterion of self-interest. Such an assumption would clearly be out of place in an evolutionary context. Instead, the criterion of rationality is replaced by that of population dynamics and stability, and the criterion of self-interest by Darwinian fitness."

"Evolutionary game theory is a way of thinking about evolution at the phenotypic level when the fitnesses of particular phenotypes depend on their frequencies in the population."

"Paradoxically, it has turned out that game theory is more readily applied to biology than to the field of economic behavior for which it was originally designed"

"The last decade has seen a steady increase in the application of concepts from the theory of games to the study of evolution. Fields as diverse as sex ratio theory, animal distribution, contest behaviour and reciprocal altruism have contributed to what is now emerging as a universal way of thinking about phenotypic evolution."

"This man is a genius."

"... he gave his name to the Nash equilibrium – a position in a situation of competition or conflict in which both sides have selected a strategy, but where neither side can then independently change their strategy without ending up in a less desirable position. Such positions are common in everyday life, and in the interactions of business people, politicians and nations. He earned his early reputation, and his 1994 Nobel prize in economics, by proving mathematically that there is at least one Nash equilibrium lying in wait to trap us in every situation of competition or conflict where the parties are unwilling or unable to communicate."

"He was always full of mathematical ideas, not only on game theory, but in geometry and topology as well. However, my most vivid memory of this time is of the many games which were played in the common room. I was introduced to Go and Kriegspiel, and also to an ingenious topological game which we called Nash in honor of the inventor."

"As I said, I spent a great deal of time in the common room, and so did Nash. He was a very interesting character and full of ideas. He also used to wander in the corridors whistling things like Bach, which I had never really heard before — a strange way to be introduced to classical music! I saw quite a bit of him over those years and I also became interested in game theory, in which he was an important contributor. He was a very interesting person."

"When Freeman Dyson, the physicist, greeted John Forbes Nash, Jr. at the Institute for Advanced Study one day in the early 1990s, he hardly expected a response. A mathematics legend in his twenties, Nash had suffered for decades from a devastating mental illness. A mute, ghost-like figure who scrawled mysterious messages on blackboards and occupied himself with numerological calculations, he was known around Princeton only as “the Phantom.” To Dyson’s astonishment, Nash replied. He’d seen Dyson’s daughter, an authority on computers, on the news, he said. “It was beautiful,” recalled Dyson. “Slowly, he just somehow woke up.” Nash’s miraculous emergence from an illness long considered a life sentence was neither the first, nor last, surprise twist in an extraordinary life."

"[W]hile the book and the movie probed the conflicting complexities in Nash the man, neither delved deeply into Nash's math. So for most people today, his accomplishments remain obscure. Within the world of science, though, Nash's math now touches more disciplines than Newton's or Einstein's. What Newton's or Einstein's math did for the physical universe, Nash's math may now be accomplishing for the biological and social universe."

"The tools introduced by Nash gave rise to new powerful theories (convex integration, Nash-Moser scheme) which later would allow to attack many mathematical problems."

"A less obvious type of application (of non-cooperative games) is to the study of . By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration."

"The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation. The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games."

"We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other."

"I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium and symptoms of schizophrenia."

"By the time I was a student in high school I was reading the classic Men of Mathematics by E. T. Bell and I remember succeeding in proving the classic Fermat theorem about an integer multiplied by itself p times where p is a prime."

"As a graduate student I studied mathematics fairly broadly and I was fortunate enough, besides developing the idea which led to "," also to make a nice discovery relating to manifolds and real algebraic varieties. So I was prepared actually for the possibility that the game theory work would not be regarded as acceptable as a thesis in the mathematics department and then that I could realize the objective of a Ph. D. thesis with the other results."

"Gradually I began to intellectually reject some of the delusionally influenced lines of thinking which had been characteristic of my orientation. This began, most recognizably, with the rejection of politically-oriented thinking as essentially a hopeless waste of intellectual effort."

"At the present time I seem to be thinking rationally again in the style that is characteristic of scientists. However this is not entirely a matter of joy as if someone returned from physical disability to good physical health. One aspect of this is that rationality of thought imposes a limit on a person's concept of his relation to the cosmos."

"Statistically, it would seem improbable that any mathematician or scientist, at the age of 66, would be able through continued research efforts, to add much to his or her previous achievements. However I am still making the effort and it is conceivable that with the gap period of about 25 years of partially deluded thinking providing a sort of vacation my situation may be atypical. Thus I have hopes of being able to achieve something of value through my current studies or with any new ideas that come in the future."

"Though I had success in my research both when I was mad and when I was not, eventually I felt that my work would be better respected if I thought and acted like a 'normal' person."

"People are always selling the idea that people with mental illness are suffering. I think madness can be an escape. If things are not so good, you maybe want to imagine something better. In madness, I thought I was the most important person in the world."

"You don't have to be a mathematician to have a feel for numbers. A movie, by the way, was made — sort of a small-scale offbeat movie — called Pi recently. I think it starts off with a big string of digits running across the screen, and then there are people who get concerned with various things, and in the end this Bible code idea comes up. And that ties in with numbers, so the relation to numbers is not necessarily scientific, and even when I was mentally disturbed, I had a lot of interest in numbers."