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Game theory is a formal way of analyzing competitive or cooperative interactions among people who are making decisions-whether on a game board or in society at large. Starting simply, we can draw some generalizations about common games such as tic-tac-toe or chess. These games are said to have perfect information because all the rules, possible choices and past history of play are known to all participants. That means players can win such games by using a pure strategy, which is an overall plan that specifies moves to be taken in all eventualities that can arise in play. Games without perfect information, such as stone-paper-scissors or poker, offer no pure strategy that ensures a win. If a player employs one strategy too often, his or her opponent will catch on. This is where the modern mathematical theory of games comes into play. It offers insights regarding optimal mixes of strategies and the frequency with which one can expect to win.
Stone-paper-scissors is called a two-person zero-sum game, because any money one player wins, the other loses. Mathematician John von Neumann proved that all two-person zerosum games have optimal strategies for both players. Such a game is said to be fair if both players can expect to win nothing over a long run of plays, as is the case in stone-paper-scissors, although not all zero-sum games are fair.