Avinash K Dixit - Collected Quotes

"A game is a situation of strategic interdependence: the outcome of your choices (strategies) depends upon the choices of one or more other persons acting purposely. The decision makers involved in a game are called players, and their choices are called moves. The interests of the players in a game may be in strict conflict; one person’s gain is always another’s loss. Such games are called zero-sum. More typically, there are zones of commonality of interests as well as of conflict and so, there can be combinations of mutually gainful or mutually harmful strategies. Nevertheless, we usually refer to the other players in a game as one’s rivals." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"Chess experts have been successful at characterizing optimal strategies near the end of the game. Once the chessboard has only a small number of pieces on it, experts are able to look ahead to the end of the game and determine by backward reasoning whether one side has a guaranteed win or whether the other side can obtain a draw. But the middle of the game, when several pieces remain on the board, is far harder. Looking ahead five pairs of moves, which is about as much as can be done by experts in a reasonable amount of time, is not going to simplify the situation to a point where the endgame can be solved completely from there on." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"Chess strategy illustrates another important practical feature of looking forward and reasoning backward: you have to play the game from the perspective of both players. While it is hard to calculate your best move in a complicated tree, it is even harder to predict what the other side will do." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"John Nash’s beautiful equilibrium was designed as a theoretical way to square just such circles of thinking about thinking about other people’s choices in games of strategy. The idea is to look for an outcome where each player in the game chooses the strategy that best serves his or her own interest, in response to the other’s strategy. If such a configuration of strategies arises, neither player has any reason to change his choice unilaterally. Therefore, this is a potentially stable outcome of a game where the players make individual and simultaneous choices of strategies." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"Many mathematical game theorists dislike the dependence of an outcome on historical, cultural, or linguistic aspects of the game or on purely arbitrary devices like round numbers; they would prefer the solution be determined purely by the abstract mathematical facts about the game - the number of players, the strategies available to each, and the payoffs to each in relation to the strategy choices of all. We disagree. We think it entirely appropriate that the outcome of a game played by humans interacting in a society should depend on the social and psychological aspects of the game." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"Science and art, by their very nature, differ in that science can be learned in a systematic and logical way, whereas expertise in art has to be acquired by example, experience, and practice." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"Strategic thinking starts with your basic skills and considers how best to use them. Knowing the law, you must decide the strategy for defending your client. Knowing how well your football team can pass or run and how well the other team can defend against each choice, your decision as the coach is whether to pass or to run. Sometimes, as in the case of nuclear brinkmanship, strategic thinking also means knowing when not to play." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"The essence of a game of strategy is the interdependence of the players’ decisions. These interactions arise in two ways. The first is sequential [...] The players make alternating moves. [...] The second kind of interaction is simultaneous, as in the prisoners’ dilemma [...] The players act at the same time, in ignorance of the others’ current actions. However, each must be aware that there are other active players, who in turn are similarly aware, and so on. Therefore each must figuratively put himself in the shoes of all and try to calculate the outcome. His own best action is an integral part of this overall calculation. When you find yourself playing a strategic game, you must determine whether the interaction is simultaneous or sequential." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

"When playing mixed or random strategies, you can’t fool the opposition every time. The best you can hope for is to keep them guessing and fool them some of the time. You can know the likelihood of your success but cannot say in advance whether you will succeed on any particular occasion. In this regard, when you know that you are talking to a person who wants to mislead you, it may be best to ignore any statements he makes rather than accept them at face value or to infer that exactly the opposite must be the truth." (Avinash K Dixit & Barry J Nalebuff, "The Art of Strategy: A Game Theorist's Guide to Success in Business and Life", 2008)

On Strategy I

"It is possible to learn strategic flexibility [...] however, that it is difficult to teach it. It is not a matter of learning a few readily grasped general principles, but of learning a lot of small, 'local' rules, each of which is applicable in a limited area. The point is not to learn how to drive a steamroller with which one can flatten all problems in the same way, but to learn the adroitness of a puppeteer, who at one time holds many strings in his hands and who is able to adapt his movements to the given circumstances in the most sophisticated ways." (Dietrich Dörner, "The Logic of Failure", Philosophical Transactions of the Royal Society of London (B), 1990)

"[…] a rule for choosing an action is termed a strategy. If the rule says to always take the same action, it's called a pure strategy; otherwise, the strategy is called mixed. A solution to a game is simply a strategy for each player that gives each of them the best possible payoff, in the sense of being a regret-free choice." (John L Casti, "Five Golden Rules", 1995)

"So the strategy of mixing the choices with equal likelihood is an equilibrium point for the game, in the same sense that the minimax point is an equilibrium for a game having a saddle point. Thus, using a strategy that randomizes their choices, Max and Min can each announce his or her strategy to the other without the opponent being able to exploit this information to get a larger average payoff for himself or herself." (John L Casti, "Five Golden Rules", 1995)

"A strategy is usually expressed by a set of heuristic rules. The heuristic rules ease the process of searching for an optimal solution. The process is usually iterative and at one step either the global optimum for the whole problem (state) space is found and the process stops, or a local optimum for a subspace of the state space of the problem is found and the problem continues, if it is possible to improve." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"Strategy in complex systems must resemble strategy in board games. You develop a small and useful tree of options that is continuously revised based on the arrangement of pieces and the actions of your opponent. It is critical to keep the number of options open. It is important to develop a theory of what kinds of options you want to have open." (John H Holland, [presentation] 2000)

"[...] a general-purpose universal optimization strategy is theoretically impossible, and the only way one strategy can outperform another is if it is specialized to the specific problem under consideration." Yu-Chi Ho & David L Pepyne, "Simple explanation of the no-free-lunch theorem and its implications", Journal of Optimization Theory and Applications 115, 2002)

"[...] the System may be so thoroughly organized around the familiar response strategy that a new response would require extensive restructuring - something that Systems do with the greatest reluctance and difficulty." (John Gall, "Systemantics: The Systems Bible", 2002)

"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)

"A heuristic is a strategy we derive from previous experience with a similar problem." (Darius Foroux, "Think Straight", 2017)