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Game Theory

Game theory is mainly applied in areas such as psychology, logic, biology, economics, and political science. This is a report on game theory with particular focus given to its applications, benefits and limitations, and other aspects. Game Theory Game theory or alternatively interactive decision theory is based on the fundamental concept of zero-sum games, where gains of an individual are exactly to the net losses of other participants. The game theory can be applicable to a range of behavioral relations. According to the game theory, a game must specify four essential elements such as players of the game, information and actions (which are available for decision making), and payoffs for each outcome (Game Theory). The two main branches of game theory include cooperative and non-cooperative game theory. When the non-cooperative games are illustrated in the extensive and normal forms, characteristic function form is used to present most cooperative games. According to Fudenberg and Tirole, in the extensive form, games are played using trees (see figure 1) and each node (vertex) indicates a player’s point of choice. Each player is clearly specified with a number represented by the vertex (67). The player’s possible action is indicated by the lines out of the vertex whereas the payoffs are presented at the bottom of the tree. The extensive form can be regarded as “a multi-player generalizations of a decision tree” (Fudenberg and Tirole 67). This is illustrated in the figure 1. Figure 1 The figure is taken from Ross, Don, "Game Theory", The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), In contrast to the extensive form, a matrix indicating players, strategies and payoffs are used to represent the normal form or strategic form. As Jian et al point out, in general any function which is associated with a payoff for each player with all combination of actions can be used to represent the normal form. When the normal form is used to define a game, it is assumed that each player acts without actually knowing the actions of others. If the players are aware of the action of other players, the game is usually illustrated using the extensive form. The origin of the characteristic function form is found in the book written by John von Neumann and Oskar Morgenstern. The authors guessed that when a union C emerges, it functions against the fraction (N/C) as if a normal game is played by two individuals. Here, the balanced payoff of C is identified as the basic function. Examples of Game Theory One of the most commonly cited examples of game theory is the prisoner’s dilemma. Suppose that two brokers, Robinson and Thomas, have been accused of fraudulent trading activities and arrested. Both of them are being questioned separately and hence they do not know what the other is going to say. Robinson and Thomas want to minimize the term of imprisonment and there are four different situations. 1. If Robinson pleads that he is not guilty of the crime accused and Thomas confesses, Robinson will be jailed for a maximum term of five years and Thomas will be sentenced for a minimum of one year imprisonment. 2. If nobody confesses, then both of them will be jailed for a minimum of two years. 3. If both pleads that they are guilty of the crime accused and tries to implicate their partner, then both of the
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