# Game Theory I INTRODUCTION Game Theory, mathematical analysis of any situation involving a conflict of interest, with the intent of indicating the optimal choices that, under given conditions, will lead to a desired outcome.

Publié le 12/05/2013

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C Zero-Sum Games
A game is said to be a zero-sum game if the total amount of payoffs at the end of the game is zero.

Thus, in a zero-sum game the total amount won is exactly equal tothe amount lost.

In economic contexts, zero-sum games are equivalent to saying that no production or destruction of goods takes place within the “game economy” inquestion.

Von Neumann and Oskar Morgenstern showed in 1944 that any n-person non-zero-sum game can be reduced to an n + 1 zero-sum game, and that such n + 1 person games can be generalized from the special case of the two-person zero-sum game.

Consequently, such games constitute a major part of mathematical gametheory.

One of the most important theorems in this field establishes that the various aspects of maximal-minimal strategy apply to all two-person zero-sum games.Known as the minimax theorem, it was first proven by von Neumann in 1928; others later succeeded in proving the theorem with a variety of methods in more generalterms.
IV APPLICATIONS
Applications of game theory are wide-ranging and account for steadily growing interest in the subject.

Von Neumann and Morgenstern indicated the immediate utility oftheir work on mathematical game theory by linking it with economic behavior.

Models can be developed, in fact, for markets of various commodities with differingnumbers of buyers and sellers, fluctuating values of supply and demand, and seasonal and cyclical variations, as well as significant structural differences in theeconomies concerned.

Here game theory is especially relevant to the analysis of conflicts of interest in maximizing profits and promoting the widest distribution of goodsand services.

Equitable division of property and of inheritance is another area of legal and economic concern that can be studied with the techniques of game theory.
In the social sciences, n-person game theory has interesting uses in studying, for example, the distribution of power in legislative procedures.

This problem can be interpreted as a three-person game at the congressional level involving vetoes of the president and votes of representatives and senators, analyzed in terms ofsuccessful or failed coalitions to pass a given bill.

Problems of majority rule and individual decision making are also amenable to such study.
Sociologists have developed an entire branch of game theory devoted to the study of issues involving group decision making.

Epidemiologists also make use of gametheory, especially with respect to immunization procedures and methods of testing a vaccine or other medication.

Military strategists turn to game theory to studyconflicts of interest resolved through “battles” where the outcome or payoff of a given war game is either victory or defeat.

Usually, such games are not examples ofzero-sum games, for what one player loses in terms of lives and injuries is not won by the victor.

Some uses of game theory in analyses of political and military eventshave been criticized as a dehumanizing and potentially dangerous oversimplification of necessarily complicating factors.

Analysis of economic situations is also usuallymore complicated than zero-sum games because of the production of goods and services within the play of a given “game.”
Contributed By:Joseph Warren DaubenMicrosoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation.

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