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Prisoner's Dilemma and Life
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Game theory is the study of the characteristics and processes of games, considered as formal interactions that can be described mathematically. Thus it is a source of useful models for understanding alternatives, developing strategies and making decisions relating to a wide range of social behavior. As models, games may be used to explore the following categories: alone or in combination.
Zero-Sum. In a zero-sum game, one player's gain is another’s loss (one and minus one equal zero or, in a game such as poker, winnings are balanced by an equal amount of losses). The - players have a purely competitive relationship. In a two-person zero-sum game, there is a 'best strategy' called the minimax strategy which will minimize losses to a certain point for both parties.
Non-Zero-Sum. In a non-zero-sum game, players have at least some common interests. In a labor contract negotiation, for example, both workers and management want to get the best share of the available resources for themselves but both understand that the profitability of the firm has a substantial influence on the total amount to be divided. The non-zero-sum game includes the possibility that both parties will lose (labor and management reach a deadlock and the factory doesn't reopen after the ensuing strike) as well as that both may win and share a collaborator's surplus. Chance. In a game of chance, the outcome is determined by the laws of probability after a player has made a choice (heads or tails, odds or evens etc.) A player can play against another player who has an interest in the outcome or against ''nature” which does not. Dice, black jack and solitaire are games of chance. Skill. In a game of skill, the outcome depends on the relative abilities (knowledge, dexterity and the like) of the players. Twenty questions, ghost and golf are examples of games determined by skill. Many games and most real life situations to which game theory is applied are determined by combinations of chance and skill. Finite Games. In a finite game, the players have a limited number of choices to make and the game is over after a finite number of moves. Bridge and timed sports are examples of finite games. This is in contrast to games such as scissors/ paper/ rock which can, in principle, go on indefinitely. Games of Perfect Information. Tic-tac-toe or noughts and crosses, checkers and chess are games of perfect information.
They satisfy the conditions of strict determination: that is, there is a winning strategy which, if followed, will guarantee a win, or at least a draw for a particular player from die first move. In an actual game of chess or checkers, the number of possibilities, while finite, is too large for the human brain to hold. In tic-tac-toe, with its smaller number of moves, a winning -or at least a tie producing -strategy is demonstrable. Most card games are not games of perfect information because players do not know the contents of the pile or of their opponents' hands. Language and Metalanguage. In some games, all players speak a language in which goals and moves can be clearly understood in terms of rules and mastery of certain strategies although this does not necessarily mean that all players are equally skilled or that all have the same knowledge of the complexities of the game. In other games, some players have goals and strategies which are concealed from their opponents or even their partners. These players are speaking a metalanguage, in which their articulation of goals and strategies occurs at a level not expressible in the terms and language of the game the other players are playing. Paradoxes are frequently associated with metagames although some may be as simple as playing to tie instead of to win in order to secure a more favorable opponent in a play-off series. Faking or deception may be expressed at either the level of language or metalanguage. A game or a game theoretic analysis of a situation may combine or consider several of the above categories. A best strategy" such as the minimax strategy becomes less and less possible as the number of players and the number of options open to them increases. Mathematical models of the two person zero sum game are common but even three person games may become too complex to analyze completely.
Game theoretic models have been used in computer and manual simulations of conflicts and negotiations, to narrow the field of choices down to those worthy of serious consideration, to speed up decision making in a community or a corporation, and (at a metagame level) to study personal interaction and decision-making styles. # SOURCE von Neumann, J., & Morgenstem, O. (1953). Theory o f Games and Economic Behavior. Princeton, NJ: Princeton University Press. Rappoport, A. (1960). Fights, Games and Debates. Ann Arbor: University of Michigan Press. Rappoport, A. (1970). N-Person Game Theory. Ann Arbor: University of Michigan Press.. For a non-mathematical explanation, see: Davis, M. (1970). Game Theory. New York: Basic Books. # EXAMPLES OF A GAME • trading on the stock exchange • professional sports leagues draft of high school and college players • labor contract negotiations # EXAMPLES OF A METAGAME • employing a dummy bidder at an auction to bid up the price up on various items • personal conflict and one-up-manship behavior such as that described in Eric Berne's "Games People Play • tactical voting NON-EXAMPLES OF A GAME • the fulfillment of a contract • the creation of a work of art • a communication where the intent is to convey or elicit information # NON-EXAMPLES OF A METAGAME • any situation where all parties are consciously operating in the same context # PROBABLE ERROR • Not realizing that a game is being played • Not recognizing the difference between a metagame and other examples of apparent non-rational behavior such as incompetence or ignorance # SEE Metasystem; Metalanguage; Variety; Model