Game theorists

"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."

"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."

"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."

"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."

"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."

"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."

"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"

"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."

"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."

"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."

"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."

"That was a documentary!"

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

"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."

"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."

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

"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."

"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."

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

"Ideas are incestuous."

"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."

"There is no shortage of disputes."

"The party that negotiates in haste is often at a disadvantage."

"A mediator is an impartial outsider who tries to aid the negotiators in their quest to find a compromise agreement."

"The best practical advice then is: try to maximize your expected payoff, which is the sum of all payoffs multiplied by probabilities."

"Advice: don't embarrass your bargaining partner by forcing him or her to make all the concessions."

"Each party tended to view its own chances in court as better than the other side viewed them."

"After a little reflection, the best strategy becomes clear: bid aggressively up to a maximum cutoff value and then quit."

"It is always amazing to see how wide a spectrum of results can be obtained from replicating an identical negotiation with different principal actors; it makes no difference whether there subjects are inexperienced or whether they are senior executives and young presidents of business firms. That is an important lesson to be learned here."

"It's easy, of course, for two teams to collude, but somewhat more difficult for twenty-eight-"

"Final-offer arbitration should have great appeal for the daring (the risk seekers) who play against the timid (the risk avoiders)."

"A final word of advice: don't gloat about how well you have done."

"The art of compromise centers on the willingness to give up something in order to get something else in return. Successful artists get more than they give up."

"Most people, even in simple risky situations, don't behave the way the theory of utility would have them behave."

"the mediation of internal conflicts can be resolved by linkages with other problems."

"A lot depends on the starting point."

"We act like a zero-sum society, when in reality there is a lot of non zero-sum fat to be skimmed off to everyone's mutual advantage."

"It's worth repeating here, though, because we are talking about mechanisms for resolving conflict and many people don't realize it's impossible to devise a foolproof scheme."

"Disputants often fare poorly when they each act greedily and deceptively."

"The need is not for the creation of new analytical techniques specially designed for the negotiation process, but rather for the creative use of analytical thinking that exploits existing techniques."

"In our most Puritan of society, gambling-like other pleasures-is either taxed, restricted to certain hours, or forbidden altogether. Yet the impulse to gamble remains an eternal aspect of the irrationality of man. It finds outlets in business, war, politics, in the formal overtures of the gambling casinos, and in the less ceremonious exchanges among individuals of differing opinions."

"Shortly after pithecanthropus erectus gained the ascendancy, he turned his attention to the higher-order abstractions."

""Breaking the bank at Monte Carlo" is a euphemism for closing a single gaming table. It was last accomplished at the Casino Ste. des Bains de Mer during the final days of 1957, with a harvest of 180 million francs."

"In general statistics can be considered as the offspring of the theory of probability, it builds on its parent and extends the area of patronymic jurisdiction."

"A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution."

"The essence of the phenomenon of gambling is decision making. The act of making a decision consists of selecting one course of action, or strategy, from among the set of admissible strategies."

"There are no conventional games involving conditions of uncertainty without risk."

"The French philosopher Pierre-Hyacinthe Azaïs (1766-1845) formalized the statement that good and evil fortune are exactly balanced in that they produce for each person an equivalent result."

"Generally, a betting system for which each wager depends only on present resources and present probability of success is known as a Markov betting system."

"Coin matching and finger flashing were among the first formal games to arise in the history of gambling. The class of Morra games extends back to the pre-Christian era, although not until comparatively recent times have game-theoretic solutions been derived."

"Against human opposition the machine usually emerges victorious, since individual patterns tend to be not random but a function of emotions and previous training and experience."

"While no rigorous proof of an optimal strategy has been achieved, Robbins has proposed the principal of "staying on a winner" and has shown it to be uniformly better than a strategy of random selection."

"The hope of a positive expected gain lies in detecting a wheel with sufficient bias."

"The first-known public lottery was sponsored by Augustus Caesar to raise funds for repairing the city of Rome; the first public lottery awarding money prizes, the Lotto de Firenze, was established in Florence in 1530."

"One of the oldest mythological fables tells of Mercury playing at dice with Selene and winning from her the five days of the epact (thus totaling the 365 days of the year and harmonizing the lunar and solar calendars)."

"Although the major gambling casinos do not maintain statistical records on the results of games of Craps, one event has been recorded-that wherein a young man achieved 28 consecutive "passes" at the Desert Inn Casino, Las Vegas, Nevada (June 10, 1950). Odds against such an event are 400 million to 1."

"In 1423, the Franciscan friar St. Bernardino of Siena preached a celebrated sermon against cards (Contra Alcarum Ludos) at Bologna, attributing their invention to the devil. Despite such ecclesiastic interdiction, Johannes Gutenberg printed playing cards the same year as his famous Bible (1440). The cards from Gutenberg's press were Tarot cards, from which the modern deck is derived."

"Blackjack does possess a memory (the interdependence of the cards) and a conscience (inferior play will inevitably be penalized) and is not democratic (the mental agility and retentiveness of the player are significant factors)."

"Because the fluctuations in the composition of the deck as it is dependent over successive (and dependent) trials, it is intuitively apparent that altering decisions or the magnitude of the wager or both in accordance with the fluctuations should prove advantageous to the player."

"Contract Bridge is likely the most challenging card game extant; it is certainly the the most obsessive for its ranks of zealous followers. The initial progenitor of all Bridge forms is the game of Triumph, which gained currency about A.D. 1500. In the mid seventeenth century, Triumph evolved into Whist, a partnership game for four players. The change from Whist to Bridge occurred about 1886with a publication in London of a small pamphlet, titled Biritch or Russian Whist."

"The earliest full-length account of a chariot race appears in Book xxiii of the Iliad."

"Treatment of the apparently whimsical fluctuations of the stock quotations as truly non stationary processes requires a model of such complexity that its practical value is likely to be limited. An additional complication, not encompassed by most stock market models, arises from the manifestation of the market as a nonzero sum game."

"Reflecting an amalgam of economics, monetary, and psychological factors, the stock market represents possibly the most subtly intricate game invented by man."

"A weakness of the random-walk model lies in its assumption of instantaneous adjustment, whereas the information impelling a stock market toward its "intrinsic value" gradually becomes disseminated throughout the market place."

"From a rational standpoint, it might be expected that man should be far more willing to express financial confidence in his skills rather than risking his earnings on the mindless meanderings of chance. Experience, however, has strongly indicated the reverse proposition to hold true."

"Anthropologists have often commented on the striking resemblance between the uneducated gambler and the primitive."

"The assumption that individuals act objectively in accordance with purely mathematical dictates to maximize their gain or utility cannot be sustained by empirical observation."

"Asking who won a given war, someone has said, is like asking who won the San Francisco earthquake. That in war there is no victory but only varying degrees of defeat is a proposition that has gained increasing acceptance in the twentieth century."

"According to the first image of international relations, the locus of the important causes of war is found in the nature and behavior of man. Wars result from selfishness, from misdirected aggressive impulses, from stupidity."

"Each man does seek his own interest, but, unfortunately, not according to the dictates of reason."

"To solve these problems one needs as much an understanding of politics as an understanding of man - and the one cannot be derived from the other."

"The most important causes of political arrangements and acts are found in the nature and behavior of man."

"If we are to have peace, we must learn loyalty to a larger group. And before we can learn loyalty, the thing to which we are to be loyal must be created."

"War most often promotes the internal unity of each state involved. The state plagued by internal strife may then, instead of waiting for the accidental attack, seek the war that will bring internal peace."

"The transitory interests of royal houses may be advanced in war; the real interests of all people are furthered by the peace."

"To build a theory of international relations on accidents of geography and history is dangerous."

"Is it capitalism or states that must be destroyed in order to get peace, or must both be abolished?"

"External pressure seems to produce internal unity."

"Once socialism replaces capitalism, reason will determine the policies of states."

"With many sovereign states, with no system of law enforceable among them, with each state judging its grievances and ambitions according to the dictates of its own reason or desire - conflict, sometimes leading to war, is bound to occur."

"In anarchy there is no automatic harmony."

"States in the world are like individuals in the state of nature. They are neither perfectly good nor are they controlled by law."

"The best critical consideration of the inherent weakness of a federation of states in which the law of the federation has to be enforced on the states who are its members is contained in the Federalist Papers."

"Then what explains war among states? Rousseau's answer is really that war occurs because there is nothing to prevent it."

"In a zero-sum game, the problem is entirely one of distribution, not at all one of production."

"The implication of game theory, which is also the implication of the third image, is, however, that the freedom of choice of any one state is limited by the actions of the others."

"No system of balance functions automatically."

"War may achieve a redistribution of resources, but labor, not war, creates wealth."

"It is not true that were the Soviet Union to disappear the remaining states could easily live in peace."

"Each state pursues its own interest's, however defined, in ways it judges best. Force is a means of achieving the external ends of states because there exists no consistent, reliable process of reconciling the conflicts of interest that inevitably arise among similar units in a condition of anarchy."

"If we gather more and more data and establish more and more associations, however, we will not finally find that we know something. We will simply end up having more and more data and larger sets of correlations."

"I am not saying that such a theory cannot be constructed, but only that I cannot see how to do it in any way that might be useful. The decisive point, anyway, is that a macrotheory of international politics would lack the practical implications of macroeconomic theory. National governments can manipulate system-wide economic variables. No agencies with comparable capabilities exist internationally. Who would act on the possibilities of adjustment that a macrotheory of international politics might reveal?"

"Differences in the incidence of destruction and "death" do not account for the reluctance to refer to international politics as a harmonious realm, while competitive economies are often so described. Instead, one may say that the standards of performance now applied to international political systems are higher, or at least widely different. As John Maynard Keynes once remarked, those who believe that unhampered processes of natural selection lead to progress do not "count the cost of the struggle" (1926, p. 37). In international politics, we often count nothing but the costs of the struggle."

"Like any truly great thinker, Ken Waltz defied stereotypes. The preeminent hard-headed theorist of power politics, he savaged the hopes of those who believe that moral energy, liberal principles, or democratic crusades can end war. But he belied the common assumption that realists are callous hawks who relish the use of force. He opposed the Vietnam War, the Reagan military buildup, and the 2003 invasion of Iraq as overreactions to threats that were exaggerated and could be handled by calm containment and deterrence."

"Waltz is to the study of international relations what Darwin is to the study of biology. I make this claim in terms of the sheer intellectual significance of his theoretical contribution. One cannot make sense of the biological world apart from Darwin’s theory of evolution: equally, Waltz’s structural framework for understanding how states interact under anarchy, with an uneven distribution of power and a desire to survive, offers a powerful theory for making sense of the international system. Neither theory explains everything in their domain — one always needs to know more about particularities — but both provide compelling big-picture explanations of their domains."

"We differed on the last point, and sometimes on the key, recurring question of American foreign policy: When is military intervention justified, by which he meant, when is it in the national interest? Waltz had no patience for "liberal intervention," or what we might now call humanitarian intervention, because we could never be sure that we would succeed in making things better over the long-term. And he had little patience for supposed national security arguments that could not identify a threat to vital interests — we are not, and therefore should not act like, an empire. Waltz was not an isolationist, but he was definitely a minimalist when it came to the use of force."

"“Some have even said that Iran with nuclear weapons would stabilize the Middle East, I think people who say this have set a new standard for human stupidity.”"

""Interactive Decision Theory" would perhaps be a more descriptive name for the discipline usually called Game Theory"

"There are quite a number of novel developments intended to meet the needs of a general theory of systems. We may enumerate them in brief survey:"

"# Cybernetics, based upon the principle of feedback or circular causal trains providing mechanisms for goal-seeking and self-controlling behavior."

"# Information theory, introducing the concept of information as a quantity measurable by an expression isomorphic to negative entropy in physics, and developing the principles of its transmission."

"# Game theory, analyzing in a novel mathematical framework, rational competition between two or more antagonists for maximum gain and minimum loss."

"# , similarly analyzing rational choices, within human organizations, based upon examination of a given situation and its possible outcomes."

"# or relational mathematics, including non-metrical fields such as network and graph theory."

"# Factor analysis, i.e., isolation by way of mathematical analysis, of factors in multivariable phenomena in psychology and other fields"

"# General system theory in the narrower sense (G.S.T.), trying to derive from a general definition of “system” as complex of interacting components, concepts characteristic of organized wholes such as interaction, sum, mechanization, centralization, competition, finality, etc., and to apply them to concrete phenomena."

"Game theory is the study of individual decision-making in the face of competing boundedly rational actors."

"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory."

"A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution."

"Like all of mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises."

"That strategic rivalry in a long-term relationship may differ from that of a one-shot game is by now quite a familiar idea. Repeated play allows players to respond to each other’s actions, and so each player must consider the reactions of his opponents in making his decision. The fear of retaliation may thus lead to outcomes that otherwise would not occur. The most dramatic expression of this phenomenon is the celebrated "Folk Theorem." An outcome that Pareto dominates the point is called individually rational. The Folk Theorem asserts that any individually rational outcome can arise as a in infinitely repeated games with sufficiently little discounting."

"By the end of the war the new game theoretic methods that had been developed by von Neumann and Morgenstern were added to the toolkit and mathematical techniques that operations research scientists deployed. These proved very valuable, and game theoretic approaches took on great importance after the war."

"Game theory is about how people cooperate as much as how they compete... Game theory is about the emergence, transformation, diffusion and stabilization of forms of behavior."

"Game theory is logically demanding, but on a practical level, it requires surprisingly few mathematical techniques. Algebra, calculus, and basic probability theory suffice. ...the stress placed on game-theoretic rigor in recent years is misplaced. Theorists could worry more about the empirical relevance of their models and take less solace in mathematical elegance. ...[I]f a proposition is proved for a model with a finite number of agents, it is... irrelevant whether it is true for an ifinite number... There are... only a finite number of people, or even bacteria. Similarly, if something is true in games in which payoffs are finitely divisible... it does not matter whether it is true when payoffs are infinitely divisible. There are no payoffs in the universe... infinitely divisible. Even time... continuous in principle, can be measured only by devices with a finite number of s. Of course, models based on the real and complex numbers can be hugely useful, but they are just approximations... There is... no intrinsic value of a theorem that is true for a continuum of agents on a , if it is also true for a finite number of agents of a finite choice space."

"Direct application of the theory of games to the solution of real problems has been rare, and its chief uses have been to offer some insight and understanding into the problems of competition (without actually solving them), and to provide mathematicians with new fields to conquer. Many important real problems involve more than two opponents, are not zero-sum, and exceed the bounds of the most developed versions of game theory."

"Chapter 2 describes the most demanding rational choice theory of all, game theory, which was developed by a genius and assumes that other people are geniuses."

"Game theory can be defined as the study of mathematical models of conflict and cooperation between intelligent rational decision-makers."

"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."

"At present game theory has, in my opinion, two important uses, neither of them related to games nor to conflict directly. First, game theory stimulates us to think about conflict in a novel way. Second, game theory leads to some genuine impasses, that is, to situations where its axiomatic base is shown to be insufficient for dealing even theoretically with certain types of conflict situations... Thus, the impact is made on our thinking process themselves, rather than on the actual content of our knowledge."

"(Game theory is) essentially a structural theory. It uncovers the logical structure of a great variety of conflict situations and describes this structure in mathematical terms. Sometimes the logical structure of a conflict situation admits rational decisions; sometimes it does not."

"[G]ame theory has already established itself as an essential tool in the , where it is widely regarded as a unifying language for investigating human behavior. Game theory's prominence in evolutionary biology builds a natural bridge between the life sciences and the behavioral sciences. And connections have been established between game theory and the two most prominent pillars of physics: and quantum theory. ...[M]any physicists, neuroscientists, and social scientists... are... pursuing the dream of a quantitative science of human behavior. Game theory is showing signs of... an increasing important role in that endeavor. It's a story of exploration along the shoreline separating the continent of knowledge from an ocean of ignorance... a story worth telling."

"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 have contributed to what is now emerging as a universal way of thinking about phenotypic evolution... 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 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 and stability, and the criterion of self-interest by Darwinian fitness."

"Mathematics is what we want to keep for ourselves. When playing games, we stick to the rules (or we are changing the game...), but when doing serious mathematics (not executing algorithms) we make up the rules—definitions, axioms... even logics. ...[I]n arithmetic we find s... a whole new 'game'... [T]o identify mathematics with games would be one of those part-for-whole mistakes (like 'all geometry is projective geometry' or 'arithmetic is just logic' from the nineteenth century)... [M]y separation of game analysis from playing games tells in favour of the analogy of mathematics to analysis of games played by other... agents, and against the analogy of mathematics to the expert play of the game itself."

"One should remember that mathematical logic itself or the study of mathematics as a formal system can be considered a branch of combinatorial analysis. Metamathematics introduces a class of games—"solitaires"—to be played with symbols according to formal rules. One sense of Gödel's theorem is that some properties of these games can be ascertained only by playing them."

"The cybernetics phase of cognitive science produced an amazing array of concrete results, in addition to its long-term (often underground) influence:"

"Game theory brings to the chaos-theory table the idea that generally, societies are not designed, and that most situations don’t come with a rulebook. Instead, people have their own plans and designs on how things should fit together. They want to determine how the game is played, and they see societal designers as myopic busybodies who would imprison them with their theories."

"The implication of game theory, which is also the implication of the third image, is, however, that the freedom of choice of any one state is limited by the actions of the others."

"Right after we published our first findings, we started getting letters from all over the country saying, "You know, all you guys have done is rediscover Austrian economics"… I admit I wasn't familiar with Hayek and von Mises at the time. But now that I've read them, I can see that this is essentially true."

"Our understanding of how markets and businesses operate was passed down to us more than a century ago by a handful of European economists — Alfred Marshall in England and a few of his contemporaries on the continent. It is an understanding based squarely upon the assumption of diminishing returns: products or companies that get ahead in a market eventually run into limitations, so that a predictable equilibrium of prices and market shares is reached. The theory was roughly valid for the bulk-processing, smokestack economy of Marshall’s day. And it still thrives in today’s economics textbooks. But steadily and continuously in this century, Western economies have undergone a transformation from bulk - material manufacturing to design and use of technology — from processing of resources to processing of information, from application of raw energy to application of ideas. As this shift has occurred, the underlying mechanisms that determine economic behavior have shifted from ones of diminishing to ones of increasing returns."

"Complexity theory is really a movement of the sciences. Standard sciences tend to see the world as mechanistic. That sort of science puts things under a finer and finer microscope. In biology the investigations go from classifying organisms to functions of organisms, then organs themselves, then cells, and then organelles, right down to protein and enzymes, metabolic pathways, and DNA. This is finer and finer reductionist thinking. The movement that started complexity looks in the other direction. It’s asking, how do things assemble themselves? How do patterns emerge from these interacting elements? Complexity is looking at interacting elements and asking how they form patterns and how the patterns unfold. It’s important to point out that the patterns may never be finished. They’re open-ended. In standard science this hit some things that most scientists have a negative reaction to. Science doesn’t like perpetual novelty."

"As we begin to understand , we begin to understand that we’re part of an ever-changing, interlocking, non-linear, kaleidoscopic world."

"A technology that by chance gains an early lead in adoption may eventually 'corner the market' of potential adopters, with the other technologies becoming locked out."

"[Market outcomes] depends on the cumulation of random events."

"Where we observe the predominance of one technology or one economic outcome over its competitors we should thus be cautious of any exercise that seeks the means by which the winner's innate 'superiority' came to be translated into adoption."

"This paper has attempted to go beyond the usual static analysis of increasing-returns problems by examining the dynamical process that 'selects' an equilibrium from multiple candidates, by the interaction of economic forces and random 'historical events'. It shows how dynamically, increasing returns can cause the economy gradually to lock itself in to an outcome not necessarily superior to alternatives, not easily altered, and not entirely predictable in advance."

"The type of rationality we assume in economics — perfect, logical, deductive rationality — is extremely useful in generating solutions to theoretical problems. But it demands much of human behavior — much more in fact than it can usually deliver. If we were to imagine the vast collection of decision problems economic agents might conceivably deal with as a sea or an ocean, with the easier problems on top and more complicated ones at increasing depth, then deductive rationality would describe human behavior accurately only within a few feet of the surface. For example, the game Tic-Tac-Toe is simple, and we can readily find a perfectly rational, minimax solution to it. But we do not find rational “solutions” at the depth of Checkers; and certainly not at the still modest depths of Chess and Go."

"The inductive-reasoning system I have described above consists of a multitude of “elements” in the form of belief-models or hypotheses that adapt to the aggregate environment they jointly create. Thus it qualifies as an adaptive complex system. After some initial learning time, the hypotheses or mental models in use are mutually co-adapted. Thus we can think of a consistent set of mental models as a set of hypotheses that work well with each other under some criterion—that have a high degree of mutual adaptedness. Sometimes there is a unique such set, it corresponds to a standard rational expectations equilibrium, and beliefs gravitate into it. More often there is a high, possibly very high, multiplicity of such sets. In this case we might expect inductive reasoning systems in the economy—whether in stock-market speculating, in negotiating, in poker games, in oligopoly pricing, in positioning products in the market—to cycle through or temporarily lock into psychological patterns that may be non-recurrent, path-dependent, and increasingly complicated. The possibilities are rich."

"Conventional economic theory is built is built on the assumption of diminishing returns. Economic actions engender a negative feedback that leads to a predictable equilibrium for prices and market shares. Such feedback tends to stabilize the economy because any major changes will be offset by the very reactions they generate. The high oil prices of the 1970s encouraged energy conservation and increased oil exploration, precipitating a predictable drop in prices by the early 1980s. According to conventional theory, the equilibrium marks the “best” outcome possible under the circumstances: the most efficient use and allocation of resources."

"In many parts of the economy, stabilizing forces appear not to operate. Instead, positive feedback magnifies the effects of small economic shifts; the economic models that describe such effects differ vastly from the conventional ones. Diminishing returns imply a single equilibrium point for the economy, but positive feedback – increasing returns – makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the “best” one."

"Increasing-returns economics has roots that go back 70 years or more, but its application to the economy as a whole is largely new."

"More than anything else technology creates our world. It creates our wealth, our economy, our very way of being."

"Our deepest hope as humans lies in technology; but our deepest trust lies in nature. These forces are like tectonic plates grinding inexorably into each other in one, long, slow collision. This collision is not new, but more than anything else it is defining our era. Technology is steadily creating the dominant issues and upheavals of our time."

"Paul Krugman's attack on Brian Arthur ("The Legend of Arthur") requires a correction of its misrepresentations of fact. Arthur is a reputable and significant scholar whose work is indeed having influence in the field of industrial organization and in particular public policy toward antitrust policy in hightech industries. Krugman admits that he wrote the article because he was "just pissed off," not a very good state for a judicious statement of facts, as his column shows."

"The Economist Brian Arthur (1994) noted that it is impossible for people to reason deductively in complex situations; there are just too many linkages of facts for anyone to keep them straight."

"Models of bounded rationality describe how a judgement or decision is reached (that is, the heuristic processes or proximal mechanisms) rather than merely the outcome of the decision, and they describe the class of environments in which these heuristics will succeed or fail."

"I was always skeptical about authority, about things which were told by authorities, because I was living in a country and in a time where the authority was utterly wrong, in my view. And therefore I distrusted, I feared authority, I also fear it today. I am in a very, very fearful, I mean maybe more than other people, but I distrust authority. That makes me more independent and also some part of rebellious,... I’m a maverick."

"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."

"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."

"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... 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 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."

"Reinhard Selten shared the 1994 Nobel Prize in economics with John Nash and john harsanyi “for their pioneering analysis of equilibria in the theory of non-cooperative games.” One problem with various Nash equilibria is that they are not always unique. Selten applied stronger conditions to reduce the number of possible equilibria and to eliminate equilibria that are unreasonable economically. In 1965 he introduced the concept of “subgame perfection,” his term for this winnowing down of possible equilibria. “At that time I did not suspect that it often would be quoted, almost exclusively for the definition of subgame perfectness,” Selten wrote in his Nobel autobiography."

"Recovery is therefore something much more elemental. It aims at continuation of life, on a simple and primitive basis. From mere survival, in view of perhaps a hundred million people killed within a few days, to the construction of a society which adheres to the lofty ideas we cherish today is a long way. And the survivors may develop ideals so different from ours that we may not recognize the country— should we live to make the comparison, or, living, should we care to make it even if we could."

"As far as the use of mathematics in economics is concerned, there is an abundance of formulas where such are not needed. They are frequently introduced, one fears, in order to show off. The more difficult the mathematical theorem, the more esoteric the name of the mathematician quoted, the better."

"Alliances are always weaker in peacetime; alliances tend to become hard and fast and strong when things are going badly... but when things are going well, cooperation is hard to achieve."

"All economic decisions, whether private or business, as well as those involving economic policy, have the characteristic that quantitative and non-quantitative information must be combined into one act of decision. It would be desirable to understand how these two classes of information can best be combined."

"Wherever mathematics has entered it has never again been pushed out by other developments. The mathematization of an area of human endeavor is not a passing fad; it is the prime mover of scientific and technological progress."

"Had it merely called to our attention the existence and exact nature of certain fundamental gaps in economic theory, the Theory of Economic Behavior by von Neumann and Morgenstern would have been a book of outstanding importance. But it does more than that. It is essentially constructive: where existing theory is considered to be inadequate, the authors put in its place a highly novel analytical apparatus designed to cope with the problem. It would be doing the authors an injustice to say that theirs is a contribution to economics only. The scope of the book is much broader. The techniques applied by the authors in tackling economic problems are of sufficient generality to be valid in political science, sociology, or even military strategy. The applicability to games proper (chess and poker) is obvious from the title. Moreover, the book is of considerable interest from a purely mathematical point of view."

"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."

"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."

"By the end of the war the new game theoretic methods that had been developed by von Neumann and Morgenstern were added to the toolkit and mathematical techniques that operations research scientists deployed. These proved very valuable, and game theoretic approaches took on great importance after the war."

"That strategic rivalry in a long-term relationship may differ from that of a one-shot game is by now quite a familiar idea. Repeated play allows players to respond to each other’s actions, and so each player must consider the reactions of his opponents in making his decision. The fear of retaliation may thus lead to outcomes that otherwise would not occur. The most dramatic expression of this phenomenon is the celebrated "Folk Theorem." An outcome that Pareto dominates the minimax point is called individually rational. The Folk Theorem asserts that any individually rational outcome can arise as a in infinitely repeated games with sufficiently little discounting."

"We investigate how the degree to which credit markets are centralized affects efficiency when there is asymmetric information. Specifically, we argue that decentralization of credit may promote efficient project selection when creditors are not fully informed ex ante about project quality. Our starting point is the idea that, although an entrepreneur (project manager) may have a relatively good idea of her project's quality from the outset, creditors acquire this information only later on, by which time the criteria for profitability may have changed. Thus, a poor project (one whose completion time is too long to be profitable ex ante) may nevertheless be financed, since a creditor cannot distinguish it at the time from a good (quick) project."

"After society has decided on a social choice rule-a recipe for choosing the optimal social alternative (or alternatives) on the basis of individuals' preferences over the set of all social alternatives-the social planner still faces the problem of how to implement that rule. In particular, the planner may not know individuals' preferences. He might attempt to elicit them, but this may not be an easy task, even abstracting from communication costs. If individuals know the rule by which the planner selects alternatives on the basis of reported preferences, they may have an incentive to report falsely."

"How could such industries as software, semiconductors, and computers have been so innovative despite historically weak patent protection? We argue that if innovation is both sequential and complementary—as it certainly has been in those industries—competition can increase firms’ future profits thus offsetting short-term dissipation of rents. A simple model also shows that in such a dynamic industry, patent protection may reduce overall innovation and social welfare. The natural experiment that occurred when patent protection was extended to software in the 1980's provides a test of this model. Standard arguments would predict that R&D intensity and productivity should have increased among patenting firms."

"It’s true that my initial training was in mathematics. However, almost by accident, I happened to take a course from Kenneth Arrow on “Information Economics,” which was so inspiring that I decided to change direction. It seemed to me that economics combined the best of both worlds: the rigor of mathematics with the immediate relevance of a social science. As for how much math I would recommend, I’d say that basic analysis, including , is certainly very useful. Also, and always helps. But beyond that, I don’t think a huge mathematical investment is necessary to do economic theory unless you are planning to work in an extremely technical area."

"The usual image of war today held by many experts as well as most laymen can be summed up in the phrase "orgiastic spasm of destruction," or, "spasm war." Many believe that if one single button is pressed all the buttons will be pressed, and that some 30 minutes or so later missiles will rain enough destruction to terminate the defender's existence as a nation; subsequently, some minutes or hours later, a similar rain of death and destruction will annihilate the attacking nation. Within perhaps an hour or two the war will be effectively over-both combatants having received death blows-with only one question left; "How bad will the radiation be for the rest of the world?""

"The Russians aren't dedicated world dominationists. You know, they just sort of want it on account of a sentimental way, you know, but not like 'By God, we got to have it!' It just doesn't make sense for them to really push too hard, you know, but just to push easy."

"He flips to a drawing of a spindly boy wearing oversized glasses, hugging an ABC primer, and sniffing a daisy. This is the enemy. " The first [mistake] is to assume that he is a sort of cretinoid idiot, who can't see, think, or anything. It might be a fair, if dangerous, assumption that the enemy is at least as stupid as we are.""

"The next picture is a Goliath with four arms, reading a book, lofting a 1000-pound dumbbell, aiming a pistol at a target, painting a picture. The enemy can do everything. "He's a giant, seven feet tall with four arms, each with two biceps. Each arm can, of course, be used simultaneously.""

"He ambles along the platform."Lots of times people say about systems analysis, why don't you guys do an experiment? What the hell are you sitting here figuring things? Why don't you go out and run an experiment? Well we'd love to run experiments,but there are two difficulties. One, in realistic experiments, people get shot down. That's not the major difficulty. We're willing to do it." The audience laughs. "We are. The real difficulty is we're talking weapons which aren't in existence yet.""

"Actually, even with tested missiles, results of attacks are not really mathematically predictable. The probability of extreme variations in performance, the upper and lower limits, cannot be calculated accurately. But laymen or narrow professionals persist in regarding the matter as a simple problem in engineering and physics."

"Even if military advantages were not to be had by deliberately limiting attack to counterforce targets, I suspect that most governments would still prefer to observe such limits. Almost nobody wants to go down in history as the first man to kill 100,000 people."

"The difference between megaton and kiloton is very large, in some ways larger than the difference between kiloton and ton. Megaton weapons are comparable to gross forces of nature, such as earthquakes and hurricanes."

"The final outcome of benevolent, informed, and intelligent decisions may turn out to be disastrous. But choices must be made; dies must be cast."

"In addition to the obvious dangers, there is another subtle but by no means minor disadvantage to a pure deterrence posture: the threat of mutual suicide is a very uninspiring concept, no matter how logical it may seem. If it happened to involve explicitly the annihilation of all humanity it would also be totally immoral; one doubts if it could long remain an important part of United States policy."

"Few people differentiate between having 10 million dead, 50 million dead, or 100 million dead. It all seems too horrible."

"I don't want to live in your world in which 1 percent of the children are born defective."My answer was rather brutal, I fear. "It is not my world,"

"Even though it is the ultimate in Type I Deterrence, the Doomsday Machine is an unsatisfactory basis for a weapon system. It is most improbable that either the Soviet or U.S.governments would ever authorize procuring such a machine. The project is expensive enough so it would be subject to a searching budgetary and operational scrutiny—a scrutiny which would raise questions it could never survive."

"(The emphasis is deliberate. This deterrent is more efficient since in most practical cases deterrents destroy populations—not decision makers.)"

"The Doomsday Machine is not sufficiently controllable. Even though it maximizes the probability that deterrence will work (including minimizing the probability of accidents or miscalculations), it is totally unsatisfactory. One must still examine the consequences of a failure. In this case a failure kills too many people and kills them too automatically. There is no chance of human intervention, control, and final decision.And even if we give up the computer and make the Doomsday Machine reliably controllable by the decision makers, it is still not controllable enough. Neither NATO nor the United States, and possibly not even the Soviet Union, would be willing to spend billions of dollars to give a few individuals this particular kind of life and death power over the entire world."

"I have been surprised at the unanimity with which the notion of the unacceptability of a Doomsday Machine is greeted. I used to be wary of discussing the concept for fear that some colonel would get out a General Operating Requirement or Development Planning Objective for the device, but it seems that I need not have worried. Except by some scientists and engineers who have overemphasized the single objective of maximizing the effectiveness of deterrence, the device is universally rejected. It just does not look professional to senior military officers, and it looks even worse to senior civilians. The fact that more than a few scientists and engineers do seem attracted to the idea is disquieting, but as long as the development project is expensive,even these dedicated experts are unlikely to get one under way."

"The unacceptability of the Doomsday Machine raises awkward, unpleasant, and complicated questions that must be considered by both policy maker and technician. If it is not acceptable to risk the lives of the three billion inhabitants of the earth in order to protect ourselves from surprise attack, then how many people would we be willing to risk? I believe that both the United States and NATO would reluctantly be willing to envisage the possibility of one or two hundred million people (i.e., about five times more than World War II deaths) dying from the immediate effects, even if one does not include deferred long-term effects due to radiation, if an all-out thermonuclear war results from a failure of Type I Deterrence. With somewhat more controversy, similar numbers would apply to Type II Deterrence. (For example, some experts would concede the statement for an all-out Soviet nuclear attack on Europe, but not if the Soviets restricted themselves to the use of conventional weapons.) We are willing to live with the possibility partly because we think of it as a remote possibility. We do not expect either kind of deterrence to fail, and we do not expect the results to be that cataclysmic if deterrence does fail."

"However, even those who expect deterrence to work might hesitate at introducing a new weapon system that increased the reliability of deterrence, but at the cost of increasing the possible casualties by a factor of 10, that is, there would then be one or two billion hostages at risk if their expectations fail. Neither the 180 million Americans nor even the half billion people in the NATO alliance should or would be willing to design and procure a security system in which a malfunction or failure would cause the death of one or two billion people. If the choice were made explicit, the United States or NATO would seriously consider "lower quality" systems; i.e.,systems which were less deterring, but whose consequences were less catastrophic if deterrence failed. They would even consider such possibilities as a dangerous degree of partial or complete unilateral disarmament, if there were no other acceptable postures. The West might be willing to procure a military system which, if used in a totally irrational and unrealistic way, could cause such damage, but only if all of the normal or practically conceivable abnormal ways of operating the system would not do anything like the hypothesized damage. On the other hand, we would not let the Soviets cynically blackmail us into accommodation by a threat on their part to build a Doomsday Machine, even though we would not consciously build a strategic system which inevitably forced the Soviets to build a Doomsday Machine in self-defense."

"Here is another form of deterrence which, while not a Doomsday Machine, is still an"ultimate" of a sort. This could be called the Homicide Pact Machine, an attempt to make a failure of Type I Deterrence mean automatic mutual homicide. The adherents to this somewhat more practical device hope to divide the work of deterrence in a natural way: We destroy the enemy and the enemy destroys us, neither of us cheating by buying any effective Counterforce as Insurance for our respective societies. The Homicide Pact Machine is clearly more satisfactory to both humanitarians and neutrals than the Doomsday Machine and both should make the distinction."

"As far as patriots and nationalists are concerned, I believe that the Homicide Pact system has many of the same drawbacks as the Doomsday Machine, though not in so extreme a form.The major advantage of the Homicide Pact is that one is not in the bizarre situation of being killed with his own equipment; while intellectuals may not so distinguish, the policy makers and practical men prefer being killed by the other side. It is just because this view no longer strikes some people as bizarre that it is so dangerous."

"I use the words "unauthorized behavior" rather than "accident" because we must guard against many types of events— psychopathic or irrational individuals, mechanical or human failure, sabotage, irresponsible behavior, and so on."

"In any case, the thought of a catastrophe or holocaust unleashed by accidental (i.e. nonhistorical) causes might be very unsettling to any Marxists who had a passionate belief in a deterministic theory of history. Instead of saying "It is inevitable that we will take over the world in fifty years", this Marxist would have to add, "Always assuming some capitalist fool doesn't press the button.""

"We must not look too dangerous to the enemy. This does not mean that we cannot do anything that threatens him. After all, our mere possession of a Type I Deterrence capability implies that we can harm him if we desire. But it does mean, to the extent that is consistent with our other objectives, we should not make him more insecure than is necessary. We do not want to make him so unhappy and distraught that he will be tempted to end his anxieties by the use of drastic alternatives. We do not wish him to conclude, "better a fearful end than endless fear." We must not appear to be excessively aggressive, irresponsible, trigger-happy, or accident prone, today or in the future."

"We must not look too dangerous to neutrals. While this is probably less important for us than not looking too dangerous to friends and allies, it is still too important to be ignored. Here again, we must not look excessively destructive. It may be all right to promise the Soviets that if they attack us we will destroy every Soviet citizen in retaliation (though personally I think this far too destructive a proposal), but we should not threaten nonbelligerents with near annihilation because of our quarrel with the Russians. Many of the world's inhabitant perhaps two-thirds of them, do not feel it is their quarrel but feel it is their world. The more destructive we look, the less they like us and our program. To the extent that some in our midst talk and threaten potential world annihilation as a U.S. defense measure, we focus undeserved attention on ourselves as being dangerous and even irresponsible—appearing to be willing to risk uncounted hundreds of millions or billions of bystanders as to our selfish ambitions and desires. Neutrals and bystanders will inevitably suffer heavily in any thermonuclear War. But there is a difference between damage and annihilation."

"In addition to not looking too dangerous to ourselves, we must not look too dangerous to our allies. This problem has many similarities with the problem of not looking too dangerous to ourselves, with one important addition—our allies must believe that being allied to us actually increases their security. Very few of our allies feel that they could survive a general war—even one fought without the use of Doomsday Machines. Therefore, to the extent that we try to use the threat of a general war to deter the minor provocations that are almost bound to occur anyway, then no matter how credible we try to make this threat, our allies will eventually find the protection unreliable or disadvantageous to them. If credible, the threat is too dangerous to be lived with. If incredible, the lack of credibility itself will make the defense seem unreliable. Therefore, in the long run the West will need "safe-looking" limited war forces to handle minor and moderate provocations. It will most likely be necessary for the U.S. to make a major contribution to such forces and to take the lead in their creation, even though there are cases where the introduction of credible and competent-looking limited war forces will make some of our allies apprehensive—at least in the short run. They will worry because such forces make the possibility of small wars seem more real, but this seems to be another case where one cannot eat his cake and have it."

"The easiest way in which one can put unintentional strains on the enemy is to have a force which looks "trigger-happy." The one circumstance under which almost all Soviet experts agree the Russians might strike is the one in which they feel they are anticipating a strike by us. It will be difficult for them to read our intentions. They will doubtless err on the side of caution. But it is not clear which side will look cautious, particularly if there is a crisis which creates apprehension. It will add a real element of stability if our posture is such that we do not look as if we have to be "trigger-happy" in order to survive. This is an important reason for not relying solely on quick reaction as a protection and for not having forces so vulnerable that we could lose most of them from a Russian first strike. Under some circumstances our vulnerability to a Russian first strike would both tempt the Russians to initiate a war and at the same time compel them, because they might feel that we would be tempted to pre empt for our own protection. If we are sufficiently vulnerable they might find it impossible to believe that we were willing, in this crisis to rely on their good will, morality; caution, or sense of responsibility as a protection."

"Equally important to not appearing "trigger-happy" is not to appear prone to either accidents or miscalculations. Who wants to live in the 1960's and 1970's in the same world with a hostile strategic force that might inadvertently start a war? Most people are not even willing to live with a friendly strategic force that may not be reliably controlled. The worst way for a country to start a war is to do it accidentally, without any preparations. That might initiate an all- out "slugging match" in which only the most alert portion of the forces gets off in the early phase. Both sides are thus likely to be clobbered," both because the initial blow was not large enough to be decisive and because the war plans are likely to be inappropriate. To repeat: On all these questions of accident, miscalculation, unauthorized behavior, trigger-happy postures, and excessive destructiveness, we must satisfy ourselves and our allies, the neutrals, and, strangely important, our potential enemies. Since it is almost inevitable that the future will see more discussion of these questions, i will be important for us not only to have made satisfactory preparations, but also to have prepared a satisfactory story. Unless every-body concerned, both laymen and experts, develops a satisfactory image of strategic forces as contributing more to security than insecurity it is most improbable that the required budgets, alliances, and intellectual efforts will have the necessary support. To the extent that people worry about our strategic forces as themselves exacerbating or creating security problems, or confuse symptoms with the disease, we may anticipate a growing rejection of military preparedness as an essential element in the solution to our security problem and a turning to other approaches not as a complement and supplement but as an alternative. In particular, we are likely to suffer from the same movement toward "responsible" budgets pacifism, and unilateral and universal disarmament that swept through England in the 1920's and 1930's. The effect then was that England prematurely disarmed herself to such an extent that she first almost lost her voice in world affairs, and later her independence in a war that was caused as much by English weakness as by anything else."

"One guy he argued with was my pal Herman Kahn, who could have won any number of Nobel Prizes, except for peace, had he stuck with science. Instead, like Pauling, he tried to save the world, especially his country, from the effects of a nuclear war he was willing to see fought."

"In college, Herman was determined to show his professors how much brighter he was in their field of expertise, which he was, and which he did to their great annoyance. In the Army, during World War II, he was equally determined to show his brilliance, from the very start at the induction center where the two of us (we were inducted at the same place on the same day) took the Army’s equivalent of an IQ test. Wanting to prove himself, Herman had boned up on every IQ test he could get his hands on. Brimming with confidence he sat next to me, certain he would score 100%, which had never happened before.“Men”, the lieutenant told us, “nobody ever has finished this test, so don’t feel under any pressure to do so. If you give the wrong answers to any of the questions it will count doubly against you, so don’t try and guess. You’ve got 45 minutes to do the best you can. Good luck. Start!” After 20 minutes or so Herman had finished. He rested for a few minutes, checked his answers, and with a few minutes left got up, turned in his paper, and left. A couple of minutes go by and Herman comes rushing back into the room demanding his paper back. “Why do you want it back?”, asked the sergeant. “Because I made an arithmetic mistake on question seventy-four (or whatever number it was) and want to correct it”, said Herman. “Get the hell out of here!”, yelled the sergeant. Herman left. Sure enough he made only one mistake, but that was enough to make him number one in the Army."

"The author of "On Escalation" is revealed not as a detached analyst, nor even as a cynically bemused observer of human folly, but rather as an enthusiastic choreographer of the dance of death. He relishes the obscene pranks he invents and the cataclysmic phantasies he invokes."

"While the group of real strategists at RAND probably never numbered more than about 25 people, the overall quality, in sheer intelligence and intellectual breadth, is simply astonishing."

"Well I certainly second that, I think in addition, well I mean other things I've written suggest reading a lot of history, and uh, clearly one of the things you want people to understand is the uncertainty of things. I mean, how you really have to look at a variety of alternative futures. Any notion that you know what's going to happen, I think is, not going to work."

"In fact, as we shall see in the next section, most attempts to explicitly measure military power are mere tabulations of forces of various sorts: the numbers of men underarms, the number of weapons of a given type, etc. This is in itself an evasion of the problem since it says nothing about the actual capabilities of the forces of one country to deal with another."

"Merely adding up all U.S. forces and comparing them with Soviet Forces, actual or potential, present or future, does not really tell one very much."

"On reflection, it is not even clear if military power is a transitive relationship. Until we have defined more explicitly how we are going to measure military power, it is not clear that if A is more powerful than B, and B more powerful than C, that A is more powerful than C."

"He is the kind of guy who attracts the attention of brilliant people and so when he was at the university of Chicago during World War II he was ruled ineligible for the draft because of a heart condition so he went to work in a munitions factory, actually weapons plant building bombers, parts for bombers but he was working with this metal shop at the university of Chicago and earn some money to pay for his education. In walks a guy who is working on his cyclotron and they haul off Marshall and he helps them fix fix it with order of magnitude improving in the cyclotron. He ends up playing bridge with a guy named Kenneth Arrow who ends up winning the Nobel prize in economics. It's one after another after another and it almost reminds you of the Forest Gump. You have this really smart guy who keeps bumping into all these fascinating people. And the other thing I guess that's quite interesting is he is sort of on the ground floor of some path breaking work on how we understand human behavior, behavior of organizations and there was a huge debate in the 1970s of how formidable the soviet union was. It was a big battle between Marshall and the CIA and he had the moral convictions to pursue that debate. In the end he was proven right. The other thing I would say, another reason we haven't heard a story he is terrible at self-promotion which is why we had to do the book instead of him. [laughter] but I used to kid and say you throw words around like manhole covers. These sorts of things but behind that sort of exterior masks a very emotional person and there are some stories in the book and I'd be glad to talk to you about them if you're interested of the deep feeling he has about other people, but the people he has mentored, many over the years and also about his country. I thought that was reflective of the other to the greatest generation."

"The essence of these tactics is some voluntary but irreversible sacrifice of freedom of choice. They rest on the paradox that the power to constrain an adversary may depend on the power to bind oneself; that, in bargaining, weakness is often strength, freedom may be freedom to capitulate, and to burn bridges behind one may suffice to undo an opponent."

"What this book is about is a kind of analysis that is characteristic of a large part of the social sciences, especially the more theoretical part. That kind of analysis explores the relation between the behavior of individuals who compromise some social aggregate, and the characteristics of the aggregate.These situations, in which people's behavior or people's choices depend on the behavior or choices of other people, are the ones that usually don't permit any simple summation or extrapolation of the aggregates. To make that connection we usually have to look at the system of interaction between individuals and their environment, that is, between individuals and other individuals or between individuals and the collectivity."

"By "market" is meant the entire complex of institutions within which people buy and sell and hire and are hired and borrow and lend and trade and contract and shop around to find bargains."

"That means that in the course of twenty years, Americans in the strategic nuclear business have gone from considering the no city strategy a preposterous one to one that is so obvious that it's taken for granted that the Soviets reciprocate the general idea. Whether this is based on any knowledge that the Soviets actually do, I don't know. My own feeling is that this is an idea that made much more sense to the Soviets than to the Americans. I think the Americans typically have rather formal, grand and honorable ideas about warfare and I think Soviet leaders are much more aware of the role of violence, brutality, ugly diplomacy, both in their internal politics and in dealing with other nations, and I don't think they have nearly as much traditional baggage about the way to use military force in war and I think if they saw that it suited their purpose to treat American cities as hostages in order to keep us from attacking their homeland populations, it might appeal to them much more quickly than it would appeal to a typical American."

"There is a distinction between an individual life and a statistical life. Let a 6-year-old girl with brown hair need thousands of dollars for an operation that will prolong her life until Christmas, and the post office will be swamped with nickels and dimes to save her. But let it be reported that without a sales tax the hospital facilities of Massachusetts will deteriorate and cause a barely perceptible increase in preventable deaths—not many will drop a tear or reach for their checkbooks."

"The most spectacular event of the past half century is one that did not occur. We have enjoyed sixty years without nuclear weapons exploded in anger."

"Arms control is so often identified with limitations on the possession or deployment of weapons that it is often overlooked that this reciprocated investment in non-nuclear capability was a remarkable instance of unacknowledged but reciprocated arms control."

"The next possessors of nuclear weapons may be Iran, North Korea, or possibly some terrorist bodies. Is there any hope that they will have absorbed the nearly universal inhibition against the use of nuclear weapons, or will at least be inhibited by the recognition that the taboo enjoys widespread acclaim?"

"There is no other science where judgements are tested in blood and answered in the servitude of the defeated, where the acknowledged authority is the leader who has won or who instills confidence that he can win."

"We will be making a sufficient but necessary contribution if we simply jar the prevalent complacency on the doctrine of shoot-from-the-hip-and-empty-the-magazine."

"It seems to me that the technique of gaming does at least two things, both of which are extremely important. One is that it tends to make a reality out of the potential and also the intentions nominally ascribed to the enemy. I have had the privilege of studying over the years a number of so-called "strategic studies," and I have often been amazed at the degree to which they are permeated by what one can only call "wishful thinking." There will often be on the first page a list of stated assumptions or postulates which will say something like the following: "(1) The enemy is very intelligent; (2) He has the initiative." When you turn the pages, however, the enemy has ceased to be intelligent, and he has also ceased to have initiative. War gaming does not let you get away with that."

"Soldiers usually are close students of tactics, but rarely are they students of strategy and practically never of war."

"In wars throughout history, events have generally proved the pre-hostilities calculations of both sides, victor as well as loser, to have been seriously wrong."

"Yet the only empirical data we have about how people conduct war and behave under its stresses is our experience with it in the past, however much we have to make adjustments for subsequent changes in conditions."

"Necessity, which frequently exists only in the mind, is less often the mother of invention than of obstinacy, and the obstinacy of those three years exacted from France a penalty which continued to exert its effects over the years, especially in World War II, and which cannot be fully summed up even now."

"Instances of grave tactical blunders are certainly not lacking in the history of war, but it is characteristic of tactical errors that tend to be self-exposing, if not in relation to some theoretical ideal then at least in relation to the best the enemy can do. In the past, it has usually been possible for strong nations to recover from them, even if at a heavy cost in blood and possibly strategic position. Strategic errors may or may not expose themselves in some obvious fashion during the course of a war, or even afterwards, and they are therefore much less likely to damage the reputations of those responsible for them."

"Clausewitz to be sure, had gone out of his way to point out that armies even when commanded by Napoleon, had rarely defeated opposing armies of as much as twice their size-thus indicating a certain boundary on the influence not only of morale but also of skill in generalship. And when greatly superior forces were defeated by lesser ones, Clausewitz hinted, it was usually because of as much owing to gross incompetence on one side as to exceptional competence on the other. Let us acknowledge the genius of blunder as well as the genius of correct action! The former appeared at least as often as the latter and has had at least as much influence on history."

"Military doctrine is universally, and has been since the time of Napoleon, imbued with the "Spirit of the Offensive." There are some very good reasons for this, which we shall review elsewhere. As with many other ideas which have a sound basis in reason, constant and fervent reiteration has created distortions, like the attitude, for example, which regards a healthy respect for enemy capabilities as defenseminded and hence ignoble."

"Brodie wasn't inhibited or shocked by matter publicists in and out of RAND flaunted as the most advanced, most modern of developments. After all, he wasn't ashamed to talk to his colleagues about his psychoanalysis. He was too snugly burrowed in his liberal arts to enjoy the gyrations of simulation. His instruments of research were antiquated: no computers, no interdisciplinary teams, just his noggin, the library, table-talk, and the occasional colloquy."

"His circle included the most prominent strategists of the period: Bernard Brodie, Albert Wohlstetter, and Thomas Schelling, among others. Virtually every substantative argument Kahn made about deterrence could be found in pages written by these men. OTW (On Thermonuclear War) was not a grotesque sideshow."