The Game Theory, instituted by John von Neumann, is essentially a mathematical process for the analysis of conflict among people or such groups of people as armies, corporations, or Bridge partnerships. It is applicable wherever a confl icting situation possesses the capability of being resolved by some form of intelligence — as in the disciplines of economics (where it commands a dominating authority), military operations, political science, psychology, law, and biology, as well as in games of Poker, Backgammon, Mahjong, inter alia. Hence the word “game” is defined as the course (playing) of a conflicting situation according to an a priori specifi ed set of rules and conventions. Games are distinguished by the number of contending interests , by the value of the winner’s reward, by the number of moves required, and by the amount of information available to the interests.
Care should be exercised to avoid confusion with the colloquial meaning of the word game . Ping-Pong and Sumo Wrestling are “games” but lie outside the domain of game theory since their resolution is a function of athletic prowess rather than intelligence (despite the fact that a minimum intelligence is requisite to understand the rules). For social conflicts, game theory should be utilized with caution and reservation. In the courtship of the village belle, for example, the competing interests might not conform to the rules agreed upon; it is also diffi cult to evaluate the payoff by a single parameter; further, a reneging of the promised payoff is not unknown in such situations. Game theory demands a sacred (and rational) character for rules of behavior that may not withstand the winds of reality. The real world, with its emotional, ethical, and social suasions, is a far more muddled skein than the Hobbesian universe of the game theorist.
The number of players or competitors in a game are grouped into distinct decision-making units, or interests (Bridge involves four players, but two interests). With n interests, a game is referred to as an n-person game. It is assumed that the value of the game to each interest can be measured quantitatively by a number, called the payoff. In practice, the payoff is usually in monetary units but may be counted in any type of exchange medium. If the payoff is transferred only among the n players participating, the game is designated a zero-sum game.
Instances where wealth is created or destroyed or a percentage of the wealth is paid to a nonparticipant are examples of non – zero-sum games in the game theory.
Tic-Tac-Toe (which involves a maximum of nine moves) and Chess (a maximum possible 5950 moves) describe a type of game wherein only a finite number of moves are possible, each of which is chosen from a finite number of alternatives. Such games are termed fi nite games, and obviously the converse situation comprises infi nitegames.
The amount of information also characterizes a game in the game theory. Competitions such as Chess, Checkers, or Shogi, where each player’s move is exposed to his opponent, are games of complete information . A variant of Chess without complete information is Kriegspiel (precise knowledge of each player’s move is withheld from his or her opponent). Bridge or Poker with all cards exposed would considerably alter the nature of that game.