“Non-Cooperative Games” is written by John Nash, Noble Laureate, and published in “The Annals of Mathematics” (Nash, 1951). The theory presented in the paper is based on an assessment of the interrelationships of available set of coalitions as a consequence of the coalitions formed due to player involved in the game. Each participant of the game acts independently, and the participants do not collaborate or coordinate with each other, which yields equilibrium point as the key ingredient. The paper begins with introduction, following list of formal definitions and terminology, which includes, finite game, mixed strategy and payoff function. The existence of equilibrium points is proved with the assistance of Kakutani’s generalization fixed point theorem. Theorem 1 states, “every finite game has an equilibrium point,” and theorem 2 states, “any finite game has a symmetric equilibrium point.” The results are generalized to ‘n’ number with each payer and position of the player structured within finite set of pure strategies. The research methods of the paper adopts developing of theory, that is, inductive reasoning for the establishment of new strategies.
The symmetry of the game is permutated with the conditioning of the strategies and followed by solutions in the next section. This section also involves three more theorems, along with proves, and it is followed with simple six examples. The section on ‘geometrical form of solutions,’ followed by dominance and contradiction methods. Last, but not the least, a real-life example of theory with the help of ‘Three-Man Poker Game;’ begins with defining five rules of the game. The paper is notable work of Dr. Nash, which ushered a new wave of research, especially in economics and other disciplines of social science.
Nash, J. F. (1951). Non-cooperative games. Annals of Mathematics, 54(2).