National Medal Of Science Laureates

"Proposition 7. If a nice strategy cannot be invaded by a single individual, it cannot be invaded by any cluster of individuals either."

"Proposition 4. For a nice strategy to be collectively stable, it must be provoked by the very first defection of the other player."

"Thus cooperation can emerge even in a world of unconditional defection. The development cannot take place if it is tried only by scattered individuals who have no chance to interact with each other. But cooperation can emerge from small clusters of discriminating individuals, as long as these individuals have even a small proportion of their interactions with each other. Moreover, if nice strategies (those which are never the first to defect) come to be adopted by virtually everyone, then those individuals can afford to be generous in dealing with any others. By doing so well with each other, a population of nice rules can protect themselves against clusters of individuals using any other strategy just as well as they can protect themselves against single individuals. But for a nice strategy to be stable in the collective sense, it must be provocable. So mutual cooperation can emerge in a world of egoists without central control by starting with a cluster of individuals who rely on reciprocity."

"Proposition 3. Any strategy which may be the first to cooperate can be collectively stable only when w is sufficiently large."

"The extraordinary success of TIT FOR TAT leads to some simple, but powerful advice: practice reciprocity. After cooperating on the first move, TIT FOR TAT simply reciprocates whatever the other player did on the previous move. This simple rule is amazingly robust. It won the first round of the Computer Tournament for the Prisoner's Dilemma by attaining a higher average score than any other entry submitted by professional game theorists. And when this result was publicized for the contestants in the second round, TIT FOR TAT won again. The victory was obviously a surprise, since anyone could have submitted it to the second round after seeing its success in the first round. But obviously people hoped they could do better-and they were wrong."

"Just as important as getting cooperation started were the conditions that allowed it to be sustainable. The strategies that could sustain mutual cooperation were the ones which were provocable."

"What makes it possible for cooperation to emerge is the fact that the players might meet again. This possibility means that the choices made today not only determine the outcome of this move, but can also influence the later choices of the players. The future can therefore cast a shadow back upon the present and thereby affect the current strategic situation. But the future is less important than the present-for two reasons. The first is that players tend to value payoffs less as the time of their obtainment recedes into the future. The second is that there is always some chance that the players will not meet again. An ongoing relationship may end when one or the other player moves away, changes jobs, dies, or goes bankrupt. For these reasons, the payoff of the next move always counts less than the payoff of the current move."

"In fact, in the Prisoner's Dilemma, the strategy that works best depends directly on what strategy the other player is using and, in particular, on whether this strategy leaves room for the development of mutual cooperation. This principle is based on the weight of the next move relative to the current move being sufHciently large to make the future important."

"Proposition 1. If the discount parameter, w, is sufficiently high, there is no best strategy independent of the strategy used by the other player."

"In this chapter Darwin's emphasis on individual advantage has been formalized in terms of game theory. This formulation establishes conditions under which cooperation in biological systems based on reciprocity can evolve even without foresight by the participants."

"The Cooperation Theory that is presented in this book is based upon an investigation of individuals who pursue their own self-interest without the aid of a central authority to force them to cooperate with each other. The reason for assuming self-interest is that it allows an examination of the difficult case in which cooperation is not completely based upon a concern for others or upon the welfare of the group as a whole. It must, however, be stressed that this assumption is actually much less restrictive than it appears."

"In addition, TIT FOR TAT was known to be a powerful competitor. In a preliminary tournament, TIT FOR TAT scored second place; and in a variant of that preliminary tournament, TIT FOR TAT won first place. All of these facts were known to most of the people designing programs for the Computer Prisoner's Dilemma Tournament, because they were sent copies of a description of the preliminary tournament. Not surprisingly, many of them used the TIT FOR TAT principle and tried to improve upon it. The striking fact is that none of the more complex programs submitted was able to perform as well as the original, simple TIT FOR TAT."

"The advice in chapter 6 to players of the Prisoner's Dilemma might serve as good advice to national leaders as well: don't be envious, don't be the first to defect, reciprocate both cooperation and defection, and don't be too clever. Likewise, the techniques discussed in chapter 7 for promoting cooperation in the Prisoner's Dilemma might also be useful in promoting cooperation in international politics. The core of the problem of how to achieve rewards from cooperation is that trial and error in learning is slow and painful. The conditions may all be favorable for long-run developments. but we may not have the time to wait for blind processes to move us slowly toward mutually rewarding strategies based upon reciprocity. Perhaps if we understand the process better, we can use our foresight to speed up the evolution of cooperation."

"What accounts for TIT FOR TAT's robust success is its combination of being nice, retaliatory, forgiving, and clear. Its niceness prevents it from getting into unnecessary trouble. Its retaliation discourages the other side from persisting whenever defection is tried. Its forgiveness helps restore mutual cooperation. And its clarity makes it intelligible to the other player, thereby eliciting long-term cooperation."

"In complex environments, individuals are not fully able to analyze the situation and calculate their optimal strategy. Instead they can be expected to adapt their strategy over time based upon what has been effective and what has not."

"Robert Axelrod's 1980 tournaments of iterated prisoner's dilemma strategies have been condensed into the slogan, Don't be too clever, don't be unfair. Press and Dyson have shown that cleverness and unfairness triumph after all."

"In the future it would be good to use these conceptual and statistical developments to answer some new questions suggested by the model. For example, the dynamics we have seen in the tribute model suggest the following interesting questions: a. What are the minimal conditions for a new actor to emerge? b. What tends to promote such emergence? c. How are the dynamics affected by the number of elementary actors? d. What can lead to collapse of an aggregate actor? e. How can new actors grow in the shadow of established actors?"

"2. Change the payoffs A common reaction of someone caught in a Prisoner's Dilemma is that "there ought to be a law against this sort of thing." In fact, getting out of Prisoner's Dilemmas is one of the primary functions of government: to make sure that when individuals do not have private incentives to cooperate, they will be required to do the socially useful thing anyway. Laws are passed to cause people to pay their taxes, not to steal, and to honor contracts with strangers. Each of these activities could be regarded as a giant Prisoner's Dilemma game with many players."

"The social influence model illustrates three fundamental points: 1. Local convergence can lead to global polarization. 2. The interplay between different features of culture can shape the process of social influence. 3. Even simple mechanisms of change can give counterintuitive results, as shown by the present model, in which large territories generate surprisingly little polarization."

"Aggregation means the organization of elements of a system into patterns that tend to put highly compatible elements together and less compatible elements apart. Landscape theory predicts how aggregation will lead to alignments among actors (such as nations), whose leaders are myopic in their assessments and incremental in their actions. The predicted configurations are based upon the attempts of actors to minimize their frustration based upon their pairwise propensities to align with some actors and oppose others. These attempts lead to a local minimum in the energy landscape of the entire system. The theory is supported by the results of the alignment of seventeen European nations in the Second World War. The theory has potential for application to coalitions of business firms, political parties in parliaments, social networks, social cleavages in democracies, and organizational structures."

"Tournament studies, ecological simulation, and theoretical analysis demonstrate: (1) A generous version of tit for tat is a highly effective strategy when the players it meets have not adapted to noise; (2) If the other players have adapted to noise, a contrite version of tit for tat is even more effective at quickly restoring mutual cooperation without the risk of exploitation; (3) Pavlov is not robust."

"To be believable, an optimism must first acknowledge fundamental reality, including the reality of human nature, but also the nature of all life. Life as we know it, and probably throughout the universe if there is life elsewhere, means Darwinian life. In a Darwinian world, that which survives survives, and the world becomes full of whatever qualities it takes to survive. As Darwinians, we start pessimistically by assuming deep selfishness at the level of natural selection, pitiless indifference to suffering, ruthless attention to individual success at the expense of others. And yet from such warped beginnings, something can come that is in effect, if not necessarily in intention, dose to amicable brotherhood and sisterhood. This is the uplifting message of Robert Axelrod's remarkable book."

"A major goal of investigating how cooperative norms in societal settings have been established is a better understanding of how to promote cooperative norms in international settings. This is not as utopian as it might seem because international norms against slavery and colonialism are already strong, while international norms are partly effective against racial discrimination, chemical warfare, and the proliferation of nuclear weapons. Because norms sometimes become established surprisingly quickly, there may be some useful cooperative norms that could be hurried along with relatively modest interventions."

"The two-person iterated Prisoner’s Dilemma is the E. coli of the social sciences, allowing a very large variety of studies to be undertaken in a common framework."

"Throughout the social sciences today, the dominant form of modeling is based upon the rational-choice paradigm. Game theory, in particular, is typically based upon the assumption of rational choice. In my view, the reason for the dominance of the rational-choice approach is not that scholars think it is realistic. Nor is game theory used solely because it offers good advice to a decision maker, because its unrealistic assumptions undermine much of its value as a basis for advice."

"Four factors are examined which can give rise to interesting types of social structure: labels, reputation, regulation, and territoriality. A label is a fixed characteristic of a player, such as sex or skin color, which can be observed by the other player. It can give rise to stable forms of stereotyping and status hierarchies. The reputation of a player is malleable and comes into being when another player has information about the strategy that the first one has employed with other players. Reputations give rise to a variety of phenomena. including incentives to establish a reputation as a bully, and incentives to deter others from being bullies. Regulation is a relationship between a government and the governed. Governments cannot rule only through deterrence, but must instead achieve the voluntary compliance of the majority of the governed. Therefore regulation gives rise to the problems of just how stringent the rules and the enforcement procedures should be. Finally, territoriality occurs when players interact with their neighbors rather than with just anyone. It can give rise to fascinating patterns of behavior as strategies spread through a population."

"A moral of the story is that models that aim to explore fundamental processes should be judged by their fruitfulness, not by their accuracy. For this purpose, realistic representation of many details is unnecessary and even counterproductive."

"Proposition 2. TIT FOR TAT is collectively stable if and only if, w is large enough. This critical value of w is a function of the four payoff parameters, T; R, P, and S."

"The first American edition of The Evolution of Cooperation was published in 1984. I read it as soon as it appeared, with mounting excitement, and took to recommending it with evangelical zeal, to almost everyone I met. Everyone of the Oxford undergraduates I tutored in the years following its publication was required to write an essay on Axelrod's book, and it was one of the essays they most enjoyed writing."

"In this essay, we have developed and illustrated an approach for predicting the membership of alliances among firms developing and sponsoring products requiring technical standardization. We started with two simple and plausible assumptions, that a firm prefers (1) to join a large standardsetting alliance in order to increase the probability of successfully sponsoring a compatibility standard, and (2) to avoid allying with rivals in order to benefit individually from compatibility standards that emerge from the alliance’s efforts. We then defined the concept of utility as an approximation to profit maximization in terms of size and rivalry, and discussed the influences on incentives to ally in order to develop and sponsor standards. We showed that the Nash equilibria are the local minima of an energy function with this type of utility function."

"Hodge cohomology, algebraic de Rham cohomology, crystalline cohomology, the étale ℓ-adic cohomology theories for each prime number ℓ ... A strategy to encapsulate all the different cohomology theories in algebraic geometry was formulated initially by Alexandre Grothendieck, who is responsible for setting up much of this marvelous cohomological machinery in the first place. Grothendieck sought a single theory that is cohomological in nature that acts as a gateway between algebraic geometry and the assortment of special cohomological theories, such as the ones listed above—that acts as the motive behind all this cohomological apparatus. ..."

"Vladimir Voevodsky and his collaborators have provided us with a very interesting candidate-category of motives: a category (of sheaves relative to an extraordinarily fine Grothendieck-style topology on the category of schemes) which in some intuitive sense “softens algebraic geometry” so as to allow for a good notion of homotopy in an algebro-geometric setup and is sufficiently directly connected to concrete algebraic geometry to have already yielded some extraordinary applications. The quest for a full theory of motives is a potent driving force in complex analysis, algebraic geometry, automorphic representation theory, the study of L functions, and arithmetic. It will continue to be so throughout the current century."

"Mazur suggests that it’s possible to glimpse the essence of Grothendieck’s approach to mathematics by looking at two concepts—categories and functors. A category can be thought of almost as a grammar: take triangles, perhaps, and understand them in terms of their relationship to all other triangles. The category consists of objects, and relationships between objects. The objects are nouns and the relationships are verbs, and the category is all the ways in which they can interact. Grothendieck’s discoveries opened up mathematics in a way that was analogous to how Wittgenstein (and Saussure) changed our views of language."

"Number theory swarms with bugs, waiting to bite the tempted flower-lovers who, once bitten, are inspired to excesses of effort!"

"Sometimes the mathematical anti-Platonist believes that headway is made by showing Platonism to be unsupportable by rational means, and that it is an incoherent position to take when formulated in a propositional vocabulary. It is easy enough to throw together propositional sentences. But it is a good deal more difficult to capture a Platonic disposition in a propositional formulation that is a full and honest expression of some flesh-and-blood mathematician’s view of things. There is, of course, no harm in trying—and maybe its a good exercise. But even if we cleverly came up with a proposition that is up to the task of expressing Platonism formally, the mere fact that the proposition cannot be demonstrated to be true won’t necessarily make it vanish. There are many things—some true, some false— unsupportable by rational means."

"Discovery in mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth."

"The creative scientist lives in a 'wildness of logic,' where reason is the handmaiden and not the master."

"Bandura’s findings were particularly important in 1960s America, when lawmakers, broadcasters, and the general public were engaged in serious debate regarding the effects of television violence on the behavior of children."

"If self-efficacy is lacking, people tend to behave ineffectually, even though they know what to do."

"Persons who have a strong sense of efficacy deploy their attention and effort to the demands of the situation and are spurred by obstacles to greater effort."

"Self-belief does not necessarily ensure success, but self-disbelief assuredly spawns failure."

"I think from my experience in war and life and science, it all has made me believe that we have one life on this planet. We have one chance to live it and to contribute to the future of society and the future of life. The only "afterlife" is what other people remember of you."

"I could trace own EST brainwave to a flight back from a trip to Japan. But, of course, great ideas are often simultaneously conceived by several people who have responded in a similar way to the climate of thinking, and it can be hard to pin down when and precisely how a flash of inspiration is born. Kaplan had taught me that good ideas are a dime of dozen for a smart person, and the only thing that distinguishes good from great is in how an idea is executed—how it becomes reality. Scientific history is littered with stories of one person having an idea but not following through on it only to see another have a similar inspiration and then prove it to be valid."

"At the hearing I not only described the EST method and the rapid rate of human gene discovery but also voiced by concerns about NIH's patent efforts, a subject I was glad to get out in the open. The room went quiet as many were startled by this discovery and then Watson suddenly shouted that it was "sheer lunacy" to file such patents, adding that "virtually any monkey" could use the EST method and that he was "horrified." As Cook-Deegan, a Duke University genome discussant, described the event, "Watson was lying in wait and took aim with heavy artillery." Cook-Deegan, who was Watson's assistant at the time, told me later that Watson had practiced the lines for a week prior to the hearing."

"Moving forward in science is as much unwinding the distorted thinking of the past as it is putting a clearer idea on the table."

"Tenure actually delivers a doubly whammy to the organizations that endure this outmoded arrangement. The second-rate people who thrive in a tenured environment like nothing more than to surround themselves with more mediocrity and drive out those who might excel and reveal the shortcomings of the entrenched."

"A couple of months in the laboratory can frequently save a couple of hours in the library."

", to Frank Westheimer on presenting an idea: (Harvard Gazette)"

"This fact, that all charges are integral multiples of a fundamental unit, is still one of the unexplained puzzles of fundamental physics. It does not in any way contradict electromagnetic theory, but it is not predicted by it, and until we have a more fundamental theory that explains it, we shall not feel that we really understand electromagnetic phenomena thoroughly. Presumably its explanation will not come until we understand quantum theory more thoroughly than we do at present."

"The earth’s atmosphere is an imperfect window on the universe. Electromagnetic waves in the optical part of the spectrum (that is waves longer than X rays and shorter than radio waves) penetrate to the surface of the earth only in a few narrow spectral bands The widest of the transmitted bands corresponds roughly to the colors of visible light waves in the flanking ultraviolet and infrared regions of the optical spectrum are almost totally absorbed by the atmosphere. In addition atmospheric turbulence blurs the images of celestial objects even when they are viewed through the most powerful ground-based telescopes in an article promoting the construction of the Hubble Space Telescope."