"Game theory is designed to address situations in which the outcomes of a person’s decisions depend not just on how they choose among several options, but also on the choices made by the people with whom they interact." (David Easley & Jon Kleinberg, "Networks, Crowds, and Markets: Reasoning about a Highly Connected World", 2010)
"To understand the idea of Nash equilibrium, we should first ask why a pair of strategies that are not best responses to each other would not constitute an equilibrium. The answer is that the players cannot both believe that these strategies would actually be used in the game, since they know that at least one player would have an incentive to deviate to another strategy. So a Nash equilibrium can be thought of as an equilibrium in beliefs. If each player believes that the other player will actually play a strategy that is part of a Nash equilibrium, then she has an incentive to play her part of the Nash equilibrium.
"Analyzing the behavior of a nonlinear system is like walking through a maze whose walls rearrange themselves with each step you take" (in other words, playing the game changes the game)." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)
"Mathematicians are used to game-playing according to a set of rules they lay down in advance, despite the fact that nature always writes her own." (Philip W Anderson, "More and Different: Notes from a Thoughtful Curmudgeon", 2011)
"Natural science has discovered 'chaos'. Social science has encountered 'complexity'. But chaos and complexity are not characteristics of our new reality; they are features of our perceptions and understanding. We see the world as increasingly more complex and chaotic because we use inadequate concepts to explain it. When we understand something, we no longer see it as chaotic or complex. Maybe playing the new game requires learning a new language." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)
"Operational thinking is about mapping relationships. It is about capturing interactions, interconnections, the sequence and flow of activities, and the rules of the game. It is about how systems do what they do, or the dynamic process of using elements of the structure to produce the desired functions. In a nutshell, it is about unlocking the black box that lies between system input and system output." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)
"Mathematicians are used to game-playing according to a set of rules they lay down in advance, despite the fact that nature always writes her own. One acquires a great deal of humility by experiencing the real wiliness of nature." (Philip W Anderson, "More and Different: Notes from a Thoughtful Curmudgeon", 2011)
"Natural science has discovered 'chaos'. Social science has encountered 'complexity'. But chaos and complexity are not characteristics of our new reality; they are features of our perceptions and understanding. We see the world as increasingly more complex and chaotic because we use inadequate concepts to explain it. When we understand something, we no longer see it as chaotic or complex. Maybe playing the new game requires learning a new language." (Jamshid Gharajedaghi, "Systems Thinking: Managing Chaos and Complexity A Platform for Designing Business Architecture" 3rd Ed., 2011)
"The nice thing with Monte Carlo is that you play a game of let’s pretend, like this: first of all there are ten scenarios with different probabilities, so let’s first pick a probability. The dice in this case is a random number generator in the computer. You roll the dice and pick a scenario to work with. Then you roll the dice for a certain speed, and you roll the dice again to see what direction it took. The last thing is that it collided with the bottom at an unknown time so you roll dice for the unknown time. So now you have speed, direction, starting point, time. Given them all, I know precisely where it [could have] hit the bottom. You have the computer put a point there. Rolling dice, I come up with different factors for each scenario. If I had enough patience, I could do it with pencil and paper. We calculated ten thousand points. So you have ten thousand points on the bottom of the ocean that represent equally likely positions of the sub. Then you draw a grid, count the points in each cell of the grid, saying that 10% of the points fall in this cell, 1% in that cell, and those percentages are what you use for probabilities for the prior for the individual distributions." (Henry R Richardson) [in (Sharon B McGrayne, "The Theory That Would Not Die", 2011)]
"Chess is a perfect arena for just such an exerted exploration of the possible. Its chequered sea is very deep indeed. The mathematics behind the game’s complexity are staggering. […] For all its immensity, chess is a finite game. It is therefore at least conceivable that a machine might one day be programmed with the knowledge, deep down in its nodes, of every possible sequence of moves for every possible game. No combination, however ingenious, would ever surprise it; every board position would be as familiar as a face." (Daniel Tammet, "Thinking in Numbers" , 2012)
"The barrier to an appreciation of mathematical beauty is not insurmountable, however. […] The beauty adored by mathematicians can be pursued through the everyday: through games, and music, and magic." (Daniel Tammet, "Thinking in Numbers" , 2012)
"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." (Lawrence K Samuels, "In Defense of Chaos: The Chaology of Politics, Economics and Human Action", 2013)
"Often the key contribution of intuition is to make us aware of weak points in a problem, places where it may be vulnerable to attack. A mathematical proof is like a battle, or if you prefer a less warlike metaphor, a game of chess. Once a potential weak point has been identified, the mathematician’s technical grasp of the machinery of mathematics can be brought to bear to exploit it." (Ian Stewart, "Visions of Infinity", 2013)
"We can find the minimax strategy by exploiting the game’s symmetry. Roughly speaking, the minimax strategy must have the same kind of symmetry." (Ian Stewart, "Symmetry: A Very Short Introduction", 2013)
"Probability theory provides the best answer only when the rules of the game are certain, when all alternatives, consequences, and probabilities are known or can be calculated. [...] In the real game, probability theory is not enough. Good intuitions are needed, which can be more challenging than calculations. One way to reduce uncertainty is to rely on rules of thumb." (Gerd Gigerenzer, "Risk Savvy: How to make good decisions", 2014)
"The taming of chance created mathematical probability. [...] Probability is not one of a kind; it was born with three faces: frequency, physical design, and degrees of belief. [...] in the first of its identities, probability is about counting. [...] Second, probability is about constructing. For example, if a die is constructed to be perfectly symmetrical, then the probability of rolling a six is one in six. You don’t have to count. [...] Probabilities by design are called propensities. Historically, games of chance were the prototype for propensity. These risks are known because people crafted, not counted, them. [...] Third, probability is about degrees of belief. A degree of belief can be based on anything from experience to personal impression." (Gerd Gigerenzer, "Risk Savvy: How to make good decisions", 2014)
"According to the traditional distinction from economics, risk is measurable, whereas uncertainty is indefinite or incalculable. In truth, risk can never be measured precisely except in dice rolls and games of chance, called a priori probability. Risk can only be estimated from observations in the real world, but to do that, we need to take a sample, and estimate the underlying distribution. In a sense, our estimates of real-world volatility are themselves volatile. Failure to realize this fundamental untidiness of the real world is called the ludic fallacy from the Latin for games. […] However, when the term risk measurement is used as opposed to risk estimation, a degree of precision is suggested that is unrealistic, and the choice of language suggests that we know more than we do. Even the language 'risk management' implies we can do more than we can." (Paul Gibbons, "The Science of Successful Organizational Change", 2015)
"Chess, with its straightforward rules and tiny Cartesian playing field, is a game tailor-made for computers." (John Horgan, "The End of Science", 2015)
"In business, as in game theory and chess, all great strategies start with a vision of the future. In one sense, the recipe is simple: it should include a sense of where the organization should go, what customers are likely to pay for, and how the organization can offer a unique product or service that customers will buy. The devil, of course, lies in the details." (David B Yoffie & Michael A Cusumano, "Strategy Rules", 2015)
"Master strategists understand that day-to-day tactical decisions are just as important as big competitive moves. Strategy creates the playing field; tactics define how you play the game - and ultimately whether you win or survive to play another day." (David B Yoffie & Michael A Cusumano, "Strategy Rules", 2015)
"Mathematicians usually think not in terms of concrete realizations but in terms of rules that are given axiomatically. Mathematics is the art of arguing with some chosen logic and some chosen axioms. As such, it is simply one of the oldest games with symbols and words." (Alfred S Posamentier & Bernd Thaller, "Numbers: Their tales, types, and treasures", 2015)
"Game theory covers an incredibly broad spectrum of scenarios of cooperation and competition, but the field began with those resembling heads-up poker: two-person contests where one player’s gain is another player’s loss. Mathematicians analyzing these games seek to identify a so-called equilibrium: that is, a set of strategies that both players can follow such that neither player would want to change their own play, given the play of their opponent. It’s called an equilibrium because it’s stable - no amount of further reflection by either player will bring them to different choices. I’m content with my strategy, given yours, and you’re content with your strategy, given mine." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"So everyone has and uses mental representations. What sets expert performers apart from everyone else is the quality and quantity of their mental representations. Through years of practice, they develop highly complex and sophisticated representations of the various situations they are likely to encounter in their fields - such as the vast number of arrangements of chess pieces that can appear during games. These representations allow them to make faster, more accurate decisions and respond more quickly and effectively in a given situation. This, more than anything else, explains the difference in performance between novices and experts." (Anders Ericsson & Robert Pool, "Peak: Secrets from the New Science of Expertise", 2016)
"The foundations of a discipline are inseparable from the rules of its game, without which there is no discipline, just idle talk. The foundations of science reside in its epistemology, meaning that they lie in the mathematical formulation of knowledge, structured experimentation, and statistical characterization of validity. Rules impose limitations. These may be unpleasant, but they arise from the need to link ideas in the mind to natural phenomena. The mature scientist must overcome the desire for intuitive understanding and certainty, and must live with stringent limitations and radical uncertainty." (Edward R Dougherty, "The Evolution of Scientific Knowledge: From certainty to uncertainty", 2016)
"The model (conceptual system) is a creation of the imagination, in accordance with the rules of the game. The manner of this creation is not part of the scientific theory. The classical manner is that the scientist combines an appreciation of the problem with reflections upon relevant phenomena and, based on mathematical knowledge, creates a model." (Edward R Dougherty, "The Evolution of Scientific Knowledge: From certainty to uncertainty", 2016)
"But chess is a limited game and every position will have patterns and markers our intuition can interpret. Each of the estimated tens of thousands of positions a strong master has imprinted in memory can also be broken down into component parts, rotated, twisted, and still be useful. Outside of the opening sequences that are indeed memorized, strong human players don’t rely on recall as much as on a super-fast analogy engine." (Garry Kasparov, "Deep Thinking", 2017)
"There is no such thing as randomness. No one who could detect every force operating on a pair of dice would ever play dice games, because there would never be any doubt about the outcome. The randomness, such as it is, applies to our ignorance of the possible outcomes. It doesn’t apply to the outcomes themselves. They are 100% determined and are not random in the slightest. Scientists have become so confused by this that they now imagine that things really do happen randomly, i.e. for no reason at all." (Thomas Stark, "God Is Mathematics: The Proofs of the Eternal Existence of Mathematics", 2018)
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