GAME ESSENCE

One-person games

In the one-person game, the simplest game of all, there is only one decision maker. Because he has no opponents to thwart him, the player need only list the options available to him and then choose one. If chance is involved, the game might seem to be more complicated, but in principle the decision is still relatively simple. A man deciding whether to carry an umbrella, for example, weighs the risks involved and makes his choice. He may make the wrong decision, but he need not be worried about being outsmarted by other players; that is, he need not take into account the decisions of others. One-person games, therefore, hold little interest for game theoreticians.

Two-person zero-sum games

Games of perfect information

The simplest game of any real theoretical interest is the finite two-person zero-sum game of perfect information. Examples of such games include chess, checkers, and the Japanese game go. In 1912 Ernst Zermelo proved that such games are strictly determined; this means that rational players making use of all available information can deduce a strategy that is clearly optimal and so the outcome of such games is preordained. In chess, for example, exactly one of three possibilities must be true: (1) white has a winning strategy (one that wins against any strategy of black); (2) black has an analogous winning strategy; or (3) white and black each have a strategy that guarantees them a win or a draw. (Proper play by both white and black leads to a draw.) Because a sufficiently rapid computer could analyze such games completely, they are of only minor theoretical interest.