Game Theory

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Game theory is defined as “the study of the ways in which strategic interactions among economic agents produce outcomeswith respect to thepreferences of those agents, where the outcomes in question might have been intended by none of the agents” by the Stanford Encyclopedia of Philosophy (Ross 1997). The disciplines most involved in game theory “are mathematics, economics and the other social and behavioral sciences” (McCain 1997). Game theory was created to confront the problem and provide a theory of economic and strategic behavior. In game theory, "games" have always been a metaphor for more serious interactions in human society. But game theory addresses the serious interactions using the metaphor of a game: in these serious interactions, as in games, the individual's choice is essentially a choice of a strategy, and the outcome of the interaction depends on the strategies chosen by each of the participants (McCain1997). John von Neumann a great mathematician founded game theory. The legend of John Von Neumann gives a good insight on who John Von Neumann was and his theory. John von Neumann was a child prodigy, born into a banking family in Budapest, Hungary, “when he was only six years old he could divide eight-digit numbers in his head; by 8 he had mastered calculus and by 12 he was at the graduate level in mathematics” (Halmos 1973). In 1926, at 23, he received a degree in chemical engineering in Zurich and a Ph.D. in mathematics in Budapest. From the start, mathematics provided well enough for him he quickly gained a reputation in set theory, algebra, and quantum mechanics (Halmos 1973). The start of World War II greatly changed his area of interest. According to Halmos “during and after the war, he became one of the best applied mathematicians. John von Neumann's furthered his expertise in hydrodynamics, ballistics, meteorology, game theory, and statistics". By the latter years of World War II von Neumann was playing the part of an executive management consultant, serving on several national committees, and applying his amazing ability to rapidly see through problems to their solutions. Through this means he was also a conduit between groups of scientists who were otherwise shielded from each other by the requirements of secrecy (Halmos.P, 1973). Game theory was developed in order. In the article A Chronology of Game Theory by author Paul Walker it is clear to say that in 1928 modern game theory began then was backed up with more research in 1944. In 1928 with the idea regarding the existence of mixed-strategy equilibrium in two-person zero-sum games and its proof by John von Neumann; he proved the minimax theorem in his German article "ZurTheorie der Gesellschaftsspiele" which reads "On the Theory of Parlor Games" in English (Walker 2005). Within the article it stated that “every two- person zero-sum game with finitely many pure strategies for each player is determined, ie: when mixed strategies are admitted, this variety of game has precisely one individually rational payoff vector” (Walker 2005). The paper also introduced the extensive form of a game. In 1944 the Theory of Games and Economic Behavior was published by John von Neumann and Oskar Morgenstern, the book contained work in areas of game theory such as the notion of a cooperative game, transferable utility, its coalitional form and its von Neumann-Morgenstern stable sets (Walker 2005). It was also the account of axiomatic utility theory given that led to its wide spread adoption within economics. The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty (Hamos 1973). According to McCain “games have been a scientific metaphor for a much wider range of human interactions in which the outcomes depend on the interactive strategies of two or more persons, who have opposed or at best mixed motives” (McCain 1997). Game theory is often...
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