John Nash's Game Theory

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The main purpose of game theory is to consider situations where instead of agents making decisions as reactions to exogenous prices ("dead variables"), their decisions are strategic reactions to other agents actions ("live variables"). An agent is faced with a set of moves he can play and will form a strategy, a best response to his environment, which he will play by. Strategies can be either "pure" (i.e. play a particular move) or "mixed" (random play). A " Nash Equilibrium" will be reached when each agent's actions begets a reaction by all the other agents which, in turn, begets the same initial action. In other words, the best responses of all players are in accordance with each other.

Game Theory can be roughly divided into two broad areas: non-cooperative (or strategic) games and co-operative (or coalitional) games. The meaning of these terms are self evident, although John Nash claimed that one should be able to reduce all co-operative games into some non-cooperative form. This position is what is known as the "Nash Program". Within the non-cooperative literature, a distinction can also be made between "normal" form games (static) and "extensive" form games (dynamic).

Mr. Nash came up with a much better way to look at non-zero-sum games. His method also had the advantage that it was equivalent to the von Neumann-Morgenstern analysis if the game ...