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Title: Non-Cooperative Games
Author: John Nash
Year: 1950
Abstract: This paper introduces the concept of a non-cooperative game and develops methods for the mathematical analysis of such games. The games considered are n-person games represented by means of pure strategies and pay-off functions defined for the combinations of pure strategies. The distinction between cooperative and non-cooperative games is unrelated to the mathematical description by means of pure strategies and pay-off function of a game. Tather, it depends on the possibility or impossibility of coalitions, communication, and side-payments. The concepts of an equilibrium point, a solution, a strong solution, a sub-solution, and values are introduced by mathematical definitions. And in later sections the interpretation of these concepts in non-cooperative games is dicussed. The main mathematical result is the proof of the existence in any game of at least one equilibrium point. Other results concern the geometrical structure of the set of equilibrium points of a game with a solution, the geometry of sub-solutions, and the existence of a symmetrical equilibrium point in a symmetrical game. As an illustration of the possibilitie for application a treatment of a simple three-man poker model is included.

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@PhdThesis{nash50b,
  author =	 {John Nash},
  title =	 {Non-Cooperative Games},
  school =	 {Priceton University},
  year =	 1950,
  abstract =	 {This paper introduces the concept of a
                  non-cooperative game and develops methods for the
                  mathematical analysis of such games. The games
                  considered are n-person games represented by means
                  of pure strategies and pay-off functions defined for
                  the combinations of pure strategies. The distinction
                  between cooperative and non-cooperative games is
                  unrelated to the mathematical description by means
                  of pure strategies and pay-off function of a
                  game. Tather, it depends on the possibility or
                  impossibility of coalitions, communication, and
                  side-payments. The concepts of an equilibrium point,
                  a solution, a strong solution, a sub-solution, and
                  values are introduced by mathematical
                  definitions. And in later sections the
                  interpretation of these concepts in non-cooperative
                  games is dicussed. The main mathematical result is
                  the proof of the existence in any game of at least
                  one equilibrium point. Other results concern the
                  geometrical structure of the set of equilibrium
                  points of a game with a solution, the geometry of
                  sub-solutions, and the existence of a symmetrical
                  equilibrium point in a symmetrical game. As an
                  illustration of the possibilitie for application a
                  treatment of a simple three-man poker model is
                  included.},
  keywords =     {game-theory economics},
  googleid = 	 {4Na7iac2EdYJ:scholar.google.com/},
  cluster = 	 {15425170291918886624},
  url =		 {http://jmvidal.cse.sc.edu/library/nash50b.pdf}
}
Last modified: Wed Mar 9 10:13:14 EST 2011