Game Theory

"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." (Kenneth Waltz, "Man, the State, and War", 1959)

"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. (Anatol Rapoport, "Fights, games, and debates", 1960)

"It is the shortcomings of game theory (as originally formulated) which force the consideration of the role of ethics, of the dynamics of social structure, and of social structure and of individual psychology in situations of conflict." (Anatol Rapoport, "Fights, games, and debates", 1960)

"Although the drama of games of strategy is strongly linked with the psychological aspects of the conflict, game theory is not concerned with these aspects. Game theory, so to speak, plays the board. It is concerned only with the logical aspects of strategy." (Anatol Rapoport, "The Use and Misuse of Game Theory", Scientific American 207, 1962)

"Game theory applies to a very different type of conflict, now technically called a game. The well-known games such as poker, chess, ticktacktoe and so forth are games in the strict technical Bark and counterbark sense. But what makes parlor games is not their entertainment value or detachment from real life." (Anatol Rapoport, "The Use and Misuse of Game Theory", Scientific American 207, 1962)

"Whether game theory leads to clear-cut solutions, to vague solutions, or to impasses, it does achieve
one thing. In bringing techniques of logical and mathematical analysis gives men an opportunity to bring conflicts up from the level of fights, where the intellect is beclouded by passions, to the level of games, where the intellect has a chance to operate." (Anatol Rapoport, "The Use and Misuse of Game Theory", Scientific American 207, 1962)

"[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." (Anatol Rapoport, "Prisoner's dilemma: A study in conflict and cooperation", 1965)

"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." (John M Smith, "Evolution and the Theory of Games", 1973)

"A proven theorem of game theory states that every game with complete information possesses a saddle point and therefore a solution." (Richard A Epstein, "The Theory of Gambling and Statistical Logic" [Revised Edition], 1977)

"Game theory is a collection of mathematical models designed to study situations involving conflict and/or cooperation. It allows for a multiplicity of decision makers who may have different preferences and objectives. Such models involve a variety of different solution concepts concerned with strategic optimization, stability, bargaining, compromise, equity and coalition formation." (Notices of the American Mathematical Society Vol. 26 (1), 1979) 

"Game theory is a theory of strategic interaction. That is to say, it is a theory of rational behavior in social situations in which each player has to choose his moves on the basis of what he thinks the other players' countermoves are likely to be." (John Harsanyi, "Games with Incomplete Information", 1997)

"In principle, every social situation involves strategic interaction among the participants. Thus, one might argue that proper understanding of any social situation would require game-theoretic analysis. But in actual fact, classical economic theory did manage to sidestep the game-theoretic aspects of economic behavior by postulating perfect competition, i. e., by assuming that every buyer and every seller is very small as compared with the size of the relevant markets, so that nobody can significantly affect the existing market prices by his actions." (John Harsanyi, "Games with Incomplete Information" 1997)

"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)

"Like all of mathematics, game theory is a tautology whose conclusions are true because they are contained in the premises." (Thomas Flanagan, "Game Theory and Canadian Politics", 1998)

"I think game theory creates ideas that are important in solving and approaching conflict in general." Robert Aumann, 2005)

"The players in a game are said to be in strategic equilibrium (or simply equilibrium) when their play is mutually optimal: when the actions and plans of each player are rational in the given strategic environment - i. e., when each knows the actions and plans of the others." (Robert Aumann, "War and Peace", 2005)

"An equilibrium is not always an optimum; it might not even be good. This may be the most important discovery of game theory." (Ivar Ekeland, "The Best of All Possible Worlds", 2006)

"Good decisions require that each decision-maker anticipate the decisions of the others. Game theory offers a systematic way of analysing strategic decision-making in interactive situations. [...] Game theory is not about 'playing' as usually understood. It is about conflict among rational but distrusting beings." (Geraldine Ryan & Seamus Coffey, "Games of Strategy", 2008)

"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)