Game theory

When we first hear the term 'game theory' in economics lecture, we may initially thought that it is originated in economics or perhaps some other social sciences. On the contrary, it is a branch of applied mathematics where it tries to make rationalize behavior in strategic situations, where the choice of others determines an individual's success in making choices. It is most well known in economics, especially in making strategic choice in duopoly (only two sellers), as well as other disciplines from biology, political science, international relations, computer science, and philosophy. In the game, there are three key characteristics, there is rule that determine what actions are allowable, there is strategy that players make in order to obtain their objectives in the game and there is payoffs which is the result of the interactions between the player's strategies. Game theory was first developed to analyze competitions in zero sum game where one individual does better at others' expense, ever since, it has been expanded to comprehend many types of interactions. According to Robert Aumann, today "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players (computers, animals, plants)". Traditionally, game theory seeks to establish the equilibrium in these games. In an equilibrium, the players adopt a strategy that is best for them regardless what their opponent choose and unlikely to change their strategy. Nash equilibrium and many other equilibrium concepts have been developed to get a grasp on this idea. In different fields of application, equilibrium concepts have different motivation depending on the field of application, albeit they often overlap or similar. Many criticisms and debate continue to question these methodologies especially appropriateness of particular equilibrium and the mathematical model's usefulness in general. Game theory gained prominence when the 1944 book "Theory of Games and Economic Behavior" that was written by John von Neumann in conjunction with Oskar Morgenstern was published. By 1950 it has been widely reviewed and developed by many intellectuals. Today, game theory has been recognized as an important tool in various fields.

History of game theory

The history of game theory was first documented in a letter by James Waldergrave in 1713. In the letter, he proposed the solution to a card game of Ie Her with two player with minimax mixed strategy.The fourth president of United States, James Madison made game-theoretic analysis to predict the behavior of states when they are subject to different type of taxation.

General game of theoretic analysis was not widely pursued until 1838 when Antoine Augustin Cournot's Recherches sur les principes math�matiques de la th�orie des richesses (Researches into the Mathematical Principles of the Theory of Wealth) was published. In his work, Cournot presents a solution to duopoly that is a restricted version of Nash equilibrium.

Despite many people trying to generalize the analysis, only in 1928 game theory was considered an unique field when John von Neumann published a series of his papers. Von Neumann should be regarded as the inventor of game theory even though �mile Borel, French mathematician did earlier work on games. His work in game theory peaked in 1944 book Theory of Games and Economic Behavior which analyses the method for finding mutually consistent solutions for two-person zero-sum games. He focused on cooperative game theory in this time period, which analyzes the best strategies for groups of individuals, assuming that they can collude and enforce agreement on a certain strategy. Then in 1950, RAND corporation undertake an experiment on recently appeared game that we know as the prisoner's dilemma. Nash equilibrium which is applicable to a wider variety of games than the criterion proposed by Morgenstern and von Neumann appeared around this period. On the contrary to the its predecessor, Nash equilibrium is more generalized to be able to analyze non-cooperative games in addition to cooperative games. Game theory was first applied to philosophy and political science, as well as creating the concepts of core, extensive form fame, repeated games, fictitious play and Shapley value. 15 years later, Reinhard Selten improved Nash Equilibrium by creating solution concept of subgame perfect equilibria as well as trembling hand prefection. The concept of Baynesian games and complete information was developed by John Harsanyi in late 1960s. As a result for their contributions in economic game theory, Nash, Selten and Harsanyi are awarded Nobel in Economics in 1994. In 1970, Common knowledge, trembling hand perfection and correlated equilibrium are concepts that are publicized and studied by many. At this time period, John Maynard Smith in his work evolutionary stable strategy create extensive application of game theory in biology. Robert Aumann brought about the concept of equilibrium coarsening, correlated equilibrium, and created an in-depth analysis for the consequences of common knowledge. On the other hand, Schelling worked on different aspect of game theory which is part of dynamic models and early examples of evolutionary game theory. Roger Myerson, Leonid Hurwicz and Eric Maskin created the basics of mechanism design theory which is the notion of proper equilibrium and wrote down Game Theory, Analysis of Conflict. John F. Nash, Reinhard Selten, John Harsanyi, Thomas Schelling, Robert Aumann, Roger Myerson, Leonid Hurwicz and Eric Maskin are the only 8 people that had been awarded Nobel prize in economics. Crafoord Prize was awarded to John Maynard Smith due to his contribution in creating application of game theory in biology.

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