One-Person Games
A one-person games has no real conflict of interest. Only the interest of the player in achieving a particular state of the game exists. Single-person games are not interesting from a game-theory perspective because there is no adversary making conscious choices that the player must deal with. However, they can be interesting from a probabilistic point of view in terms of their internal complexity.

Zero-Sum Games
In a zero-sum game the total possible payoffs at the end is zero since the amounts won or lost are equal. Von Neumann and Oskar Morgenstern demonstrated mathematically that n-person non-zero-sum game can be reduced to an n + 1 zero-sum game, and that such n + 1 person games can be generalized from the special case of the two-person zero-sum game. Another important theorem by Von Neumann, the minimax theorem, states certain aspects of the maximal and minimal strategies of are part of all two-person zero-sum games. Thanks to these discovery, such games are a major part of game theory.

Two-Person Games
Two-person games are the largest category of familiar games. A more complicated game derived from 2-person games is the n-person game. These games are extensively analyzed by game theorists. However, in extending these theories to n-person games a difficulty arises in predicting the interaction possible among players since opportunities arise for cooperation and collusion.

1. Dauben, Joseph W "Game Theory." Microsoft Encarta. Microsoft Corp, 1999
2. McCain, Roger A. "Game Theory: An Introductory Sketch." Hypertext. 1999 (August 1999)