"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->
1950s
Context: We give two independent derivations of our solution of the two-person cooperative game. In the first, the cooperative game is reduced to a non-cooperative game. To do this, one makes the players’ steps of negotiation in the cooperative game become moves in the noncooperative model. Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game. The negotiation process must be formalized and restricted, but in such a way that each participant is still able to utilize all the essential strengths of his position. The second approach is by the axiomatic method. One states as axioms several properties that it would seem natural for the solution to have and then one discovers that the axioms actually determine the solution uniquely. The two approaches to the problem, via the negotiation model or via the axioms, are complementary; each helps to justify and clarify the other.
“The most significant change in the games themselves is the addition of 'Follow the Follower' (p 62), a variation on the 'Mirror' game in which no one initiates and all reflect. This game quiets the mind and frees players to enter a time, space, a moment intertwined with one another in a non-physical, non-verbal, non-analytical, nonjudgmental way.”
Improvisation for the Theater 3rd Edition (1999), Viola Spolin's Preface to the Second Edition, page iv
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Viola Spolin 9
American academic and acting theorist 1906–1994Related quotes
Anatol Rapoport. (1974). Game Theory as a Theory of Conflict Resolution p. 4
1970s and later
“A less obvious type of application (of non-cooperative games) is to the study of .”
"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951); as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel
1950s
Context: A less obvious type of application (of non-cooperative games) is to the study of. By a cooperative game we mean a situation involving a set of players, pure strategies, and payoffs as usual; but with the assumption that the players can and will collaborate as they do in the von Neumann and Morgenstern theory. This means the players may communicate and form coalitions which will be enforced by an umpire. It is unnecessarily restrictive, however, to assume any transferability or even comparability of the pay-offs [which should be in utility units] to different players. Any desired transferability can be put into the game itself instead of assuming it possible in the extra-game collaboration.
Source: The Theory of Gambling and Statistical Logic (Revised Edition) 1977, Chapter Eight, Contract Bridge, p. 252
Source: "Games with Incomplete Information Played by “Bayesian” Players," 1967, p. 163: Lead paragraph's
"Non-cooperative Games" in Annals of Mathematics, Vol. 54, No. 2 (September 1951)<!-- ; as cited in Can and should the Nash program be looked at as a part of mechanism theory? (2003) by Walter Trockel -->
1950s
Context: The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form. One proceeds by constructing a model of the preplay negotiation so that the steps of negotiation become moves in a larger non-cooperative game [which will have an infinity of pure strategies] describing the total situation. This larger game is then treated in terms of the theory of this paper [extended to infinite games] and if values are obtained they are taken as the values of the cooperative game. Thus the problem of analyzing a cooperative game becomes the problem of obtaining a suitable, and convincing, non-cooperative model for the negotiation.
The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games.
“The world of shelf space is a zero-sum game: One product displaces another.”
Source: The Long Tail: Why the Future of Business Is Selling Less of More (2006), Ch. 2, p. 40
Source: The Theory of Gambling and Statistical Logic (Revised Edition) 1977, Chapter Nine, Weighted Statistical Logic And Statistical Games, p. 295
Source: "Exclusive: How Squid Game’s Hoyeon Jung Went from Model to Star of Netflix’s Biggest Hit" in Vogue https://www.vogue.com/article/squid-game-star-hoyeon-jung-interview (7 October 2021)