“A less obvious type of application (of non-cooperative games) is to the study of .”

—  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: 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.

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John Nash 23
American mathematician and Nobel Prize laureate 1928–2015

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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.

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.

Mahatma Gandhi photo

“Non-cooperation with evil is as much a duty as is cooperation with good.”

Mahatma Gandhi (1869–1948) pre-eminent leader of Indian nationalism during British-ruled India

Written statement https://babel.hathitrust.org/cgi/pt?id=mdp.39015027778375;view=1up;seq=43 in trial for sedition, March 1922
1920s

John Nash photo
Martin Luther King, Jr. photo

“But that too isn’t the way because non-cooperation with evil is as much a moral obligation as is cooperation with good.”

Martin Luther King, Jr. (1929–1968) American clergyman, activist, and leader in the American Civil Rights Movement

1950s, Loving Your Enemies (November 1957)
Source: The Autobiography of Martin Luther King, Jr.
Context: Another way is to acquiesce and to give in, to resign yourself to the oppression. Some people do that. They discover the difficulties of the wilderness moving into the promised land, and they would rather go back to the despots of Egypt because it’s difficult to get in the promised land. And so they resign themselves to the fate of oppression; they somehow acquiesce to this thing. But that too isn’t the way because non-cooperation with evil is as much a moral obligation as is cooperation with good.

Napoleon Hill photo
Jean Piaget photo

“There are therefore three types of behavior: motor behavior, egocentric behavior (with external constraint), and cooperation.”

Jean Piaget (1896–1980) Swiss psychologist, biologist, logician, philosopher & academic

Source: The Moral Judgment of the Child (1932), Ch. 1 : The Rules of the Game, § 8 : Conclusions : Motor Rules and the Two Kinds of Respect <!-- p. 86 -->
Context: A second prefatory question faces us: that of society and the individual. We have sought to contrast the child and the civilized adult on the ground of their respective social attitudes. The baby (at the stage of motor intelligence) is asocial, the egocentric child is subject to external constraint but has little capacity for cooperation, the civilized adult of to-day presents the essential character of cooperation between differentiated personalities who regard each other as equals.
There are therefore three types of behavior: motor behavior, egocentric behavior (with external constraint), and cooperation. And to these three types of social behavior there correspond three types of rules: motor rules, rules due to unilateral respect, and rules due to mutual respect.
But here again, one must beware of laying down the law: for things are motor, individual and social all at once. As we shall have occasion to show, rules of cooperation are in some respects the outcome of the rules of coercion and of the motor rules. On the other hand, coercion is applied during the first days of an infant's life, and the earliest social relations contain the germs of cooperation. Here again, it is not so much a question of these successive features themselves as of the proportions in which they are present. Moreover, the way in which conscious realization and the time-lag from one level to another come into play is a further bar to our arranging these phenomena in a strict sequence, as though they made a single appearance and then disappeared from the scene once and for all.

John Nash photo

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

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.

“The conclusions of most good operations research studies are obvious.”

Robert E. Machol (1917–1998) American systems engineer

Cited in: Paul Dickson (1999) The official rules and explanations. p. 14
Machol named this the "Billings Phenomenon". Dickson explains: "The name refers to a well-known Billings story in which a farmer becomes concerned that his black horses are eating more than his white horses. He does a detailed study of the situation and finds that he has more black horses than white horses, Machol points out."
Principles of Operations Research (1975)

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