1. In general, a game will have a certain number of players and is composed of moves, which are of two types; personal, made by one of the players, and chance, in which one of several possible outcomes is selected by a chance device acting in accordance with certain probability laws.
2. The theory of games is a method of applying mathematical logic to determine which of several strategies is likely to maximize the gain or minimize the loss of one of the players. Many economic, social, organizational, and military problems can be described in these terms, in that the other players can also choose between several strategies. It is therefore a logical procedure for formulating conservative decision rules, where the aim is to be assured of realizing the maximum of the minima gains potentially available, or to be assured of realizing the minimum of maxima losses which could be inflicted, regardless of the strategic behaviour of the other players.
3. Games that can be formulated in game-theoretic form can be usefully distinguished from operational games (described separately), which are too complex to be given a precise formulation.