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Game theory is a branch of applied mathematics which relates to strategy and prediction of behavior; a complicated science with a diverse range of applications.
While when one considers the word "game," more often than not what will spring to mind is a board game, a sport, or some other "fun" activity, when used in reference to mathematical game theory, the word becomes much more diverse, ranging from economics and political science to warfare, psychology, philosophy and even biology. Game theory is, essentially, a form of mathematics which attempts to predict behavior in any sort of "strategic" environment, whether it be the decisions made by armies on a battlefield, the trends within a financial marketplace, or the growth and development of animal species in certain environments. How Does Game Theory Work?There is nothing simple about game theory. Using complex forms of discrete mathematics, algorithms, matrices and the like, game theory is, essentially, a form of probabilistic mathematics, used to determine the optimum strategy for success under certain conditions by predicting the most probable actions of an "opponent" - or several opponents. Consider something as seemingly simple as a game of chess. One can imagine a tree diagram (known as a "game complexity diagram") which begins at the first player's turn, with 20 possible moves (2 for every pawn and two for each knight), branching the tree off in twenty directions. Then, for each of these twenty moves, the opposing player also has twenty moves, meaning that each of the twenty tree branches off another twenty times. It has been estimated that a tree diagram for a game of chess of only 10 turns would result in a tree diagram with almost 170 million possible branches! Furthermore, it has been said that there are more possible games of chess of under eighty moves than there are atoms in the universe. And it is the job of game theory to attempt to decipher strategies in games just such as this, and also in much more complicated games, which add in the endless complexity of human psychology and decision making. Most Important Applications of Game TheoryMost commonly today, the mathematics of game theory finds itself at home in the setting of economics. By analyzing market trends and company details, game theorists use laws of probability to determine likely decisions to be made by companies, and therefore which direction the market will go. As should be obvious, attempting to mathematically describe such a volatile thing as the financial market and economic conditions is a rather complicated thing, and certainly any game theorist will readily admit the fact that it is at best an imperfect science. But this does not mean game theory is not useful. By and large it certainly is. The phenomenal mathematician John Nash (the subject of the book and Oscar-winning film, A Beautiful Mind) won a Nobel Prize in economics in 1994 for his contributions to economic game theory (specifically, for his explanation of the "Nash Equilibrium"). In addition to this, seven additional game theorists have been awarded the economics prize, a testament to the value and importance of this rather intimidating branch of mathematics. References: Walker, Paul. A Chronology of Game Theory.
The copyright of the article What is Game Theory? in Math/Chaos Theory is owned by Isaac M. McPhee. Permission to republish What is Game Theory? in print or online must be granted by the author in writing.
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