“The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-person games.”

—  John Nash

"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.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "The writer has, by such a treatment, obtained values for all finite two-person cooperative games, and some special n-p…" by John Nash?
John Nash photo
John Nash 23
American mathematician and Nobel Prize laureate 1928–2015

Related quotes

John Nash photo

“The writer has developed a “dynamical” approach to the study of cooperative games based upon reduction to non-cooperative form.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

"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.

“My interest in game-theoretic problems in a narrower sense was first aroused by John Nash's four brilliant papers, published in the period 1950-53, on cooperative and on noncooperative games, on two-person bargaining games and on mutually optimal threat strategies in such games, and on what we now call Nash equilibria.”

John Harsanyi (1920–2000) hungarian economist

"John C. Harsanyi - Biographical," 1994

“Games develop personal techniques and skills necessary for the game itself, through playing. Skills are developed at the very moment a person is having all the fun and excitement playing a game has to offer--this is the exact time one is truly open to receive them.”

Viola Spolin (1906–1994) American academic and acting theorist

Improvisation for the Theater 1963), page 4

“A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.”

James P. Carse American academic

Source: Finite and Infinite Games: A Vision of Life as Play and Possibility

Vernon L. Smith photo

“One of the most intriguing discoveries of experimental economics is that (1) as we have seen, people invariably behave non-cooperatively in small and large group ‘impersonal’ market exchange institutions; (2) many (up to half in single play; over 90% in repeat play) cooperate in ‘personal’ exchange (two-person extensive form games); (3) yet in both economic environments all interactions are between anonymous players.”

Vernon L. Smith (1927) American economist

Source: "Constructivist and ecological rationality in economics," 2002, p. 528.

Jim Morrison photo

“The world becomes an apparently infinite,
yet possibly finite, card game.
Image combinations,
permutations,
comprise the world game.”

Jim Morrison (1943–1971) lead singer of The Doors

The Lords and the New Creatures: Poems (1969), The Lords: Notes on Vision

Keiji Inafune photo

“Personally when I looked around [at] all the different games at the TGS floor, I said "Man, Japan is over. We're done. Our game industry is finished."”

Keiji Inafune (1965) Japanese video game designer

Source: "TGS 09: Keiji Inafune dumps on Tokyo Game Show 2009". https://www.destructoid.com/tgs-09-keiji-inafune-dumps-on-tokyo-game-show-2009-149909.phtmlDestructoid. Retrieved 2017-08-11.

Suzanne Collins photo

“No wonder I won the games. No decent person ever does.”

Suzanne Collins book Catching Fire

Katniss, p. 117
Source: The Hunger Games trilogy, Catching Fire (2009)

John Nash photo

“Of course, one cannot represent all possible bargaining devices as moves in the non-cooperative game.”

John Nash (1928–2015) American mathematician and Nobel Prize laureate

"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.

Ambrose Bierce photo

“Monday, n. In Christian countries, the day after the baseball game.”

Ambrose Bierce book The Devil's Dictionary

The Devil's Dictionary (1911)

Related topics