games, children's, amusements or pastimes involving more than one child and in which there is some sort of formalized dramatic element, contest, or plot. Games are a cultural universal; for example, the string play called Cat's Cradle is common to cultures as varied as Eskimo, Australian, and African. Games differ from the serious pursuits of life in several ways: they are played according to tacit or explicit rules, and they are performed within a context that defines them as games (e.g., tin soldiers, house and marriage games, racing) although they may be derived from and imitative of everyday living. Because the rules vary from place to place, comparable game types are often difficult to identify precisely. Most common are contest games, in which players vie, either as individuals or as team members, to see who is best at a given activity. Such dissimilar games as I Spy, Bombardment, Red Rover, baseball, rope-jumping, tag, charades, and "Last one to the corner is a rotten egg" are all in the contest category. Amusements with predictable outcomes such as the Farmer in the Dell, often classified as games, resemble games but are considered to be children's folk drama. Game classification has been the subject of frequent and profound investigation. Among the foremost researchers in this field are the Americans Iona and Peter Opie. Some of the many types defined are games of dexterity, games of chance, showdown games, tug-of-war games, and games requiring specialized materials (jacks, marbles, mumblety-peg, dice). However, no generally useful system of classification has yet been devised. In many—if not all—cultures, formalized child's play provides a training ground where the child learns skills useful to him in later life, a counterpart to the play-training of young animals. Considerable controversy exists as to whether children's games have been to a great extent influenced by adults or whether they are passed independently from one generation of children to another. The importance of related variants and how they are transmitted are further continuing puzzles. It seems likely that complex games are developed locally from simple basic elements that have been widely diffused. Games reflect the social, economic, religious, and artistic life of the culture from which they develop and have, themselves, become an intrinsic part of human existence.

See I. and P. Opie, Children's Games in Street and Playground (1969); A. Milberg, Street Games (1976); G. Chanan and H. Francis, Toys and Games of Children of the World (1985); V. Sernaque, The Classic Children's Games (1988).

games, theory of, group of mathematical theories first developed by John Von Neumann and Oskar Morgenstern. A game consists of a set of rules governing a competitive situation in which from two to n individuals or groups of individuals choose strategies designed to maximize their own winnings or to minimize their opponent's winnings; the rules specify the possible actions for each player, the amount of information received by each as play progresses, and the amounts won or lost in various situations. Von Neumann and Morgenstern restricted their attention to zero-sum games, that is, to games in which no player can gain except at another's expense.

This restriction was overcome by the work of John F. Nash during the early 1950s. Nash mathematically clarified the distinction between cooperative and noncooperative games. In noncooperative games, unlike cooperative ones, no outside authority assures that players stick to the same predetermined rules, and binding agreements are not feasible. Further, he recognized that in noncooperative games there exist sets of optimal strategies (so-called Nash equilibria) used by the players in a game such that no player can benefit by unilaterally changing his or her strategy if the strategies of the other players remain unchanged. Because noncooperative games are common in the real world, the discovery revolutionized game theory. Nash also recognized that such an equilibrium solution would also be optimal in cooperative games. He suggested approaching the study of cooperative games via their reduction to noncooperative form and proposed a methodology, called the Nash program, for doing so. Nash also introduced the concept of bargaining, in which two or more players collude to produce a situation where failure to collude would make each of them worse off.

The theory of games applies statistical logic to the choice of strategies. It is applicable to many fields, including military problems and economics. The Nobel Memorial Prize in Economic Sciences was awarded to Nash, John Harsanyi, and Reinhard Selten (1994) and to Robert J. Aumann and Thomas C. Schelling (2005) for work in applying game theory to aspects of economics.

See J. Von Neumann and O. Morgenstern, Theory of Games and Economic Behavior (3d ed. 1953); D. Fudenberg and J. Tirole, Game Theory (1994); M. D. Davis, Game Theory: A Nontechnical Introduction (1997); R. B. Myerson, Game Theory: Analysis of Conflict (1997); J. F. Nash, Jr., Essays on Game Theory (1997); A. Rapoport, Two-Person Game Theory (1999).

Games were an important celebratory element in the religious life of ancient Greece. The modern Olympic Games take their name from the Ancient Olympic Games; the modern Olympics are divided between the Summer Olympic Games and the Winter Olympic Games.

Games in the Greco-Roman World

Ancient games in the Greco-Roman world included:

In Greece

In the Roman world

Modern Games

Modern multi-sport events, aside from the Olympics, include:

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