Game Theorists

"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."

"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."

"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."

"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."

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

"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.""

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

"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.""

"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.""

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

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

"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."

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

"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."

"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."

"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."

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

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

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

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