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Purification Theorem (physics)
In game theory, the purification theorem was contributed by Nobel laureate John Harsanyi in 1973. The theorem justifies a puzzling aspect of mixed strategy Nash equilibria: each player is wholly indifferent between each of the actions he puts non-zero weight on, yet he mixes them so as to make every other player also indifferent. The purification theorem shows how such mixed strategy equilibria can emerge even if each players plays a pure strategy, so long as players have incomplete information about the payoffs of their opponents. Such strategies arise as the limit of a series of pure strategy equilibria for a disturbed game of incomplete information, in which the payoffs of each player are known to themselves but not their opponents. The idea is that the predicted mixed strategy of the original game emerges from the ever-improving approximations of a game which is not observed by the theorist who designed the original, idealized game. The apparently mixed nature of the stra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nobel Laureate
The Nobel Prizes ( sv, Nobelpriset, no, Nobelprisen) are awarded annually by the Royal Swedish Academy of Sciences, the Swedish Academy, the Karolinska Institutet, and the Norwegian Nobel Committee to individuals and organizations who make outstanding contributions in the fields of chemistry, physics, literature, peace, and physiology or medicine. They were established by the 1895 will of Alfred Nobel, which dictates that the awards should be administered by the Nobel Foundation. The Nobel Memorial Prize in Economic Sciences was established in 1968 by the Sveriges Riksbank, the central bank of Sweden, for contributions to the field of economics. Each recipient, a Nobelist or ''laureate'', receives a gold medal, a diploma, and a sum of money which is decided annually by the Nobel Foundation. Prize Each prize is awarded by a separate committee; the Royal Swedish Academy of Sciences awards the Prizes in Physics, Chemistry, and Economics; the Karolinska Institute awards the Prize ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Harsanyi
John Charles Harsanyi ( hu, Harsányi János Károly; May 29, 1920 – August 9, 2000) was a Hungarian-American economist and the recipient of the Nobel Memorial Prize in Economic Sciences in 1994. He is best known for his contributions to the study of game theory and its application to economics, specifically for his developing the highly innovative analysis of games of incomplete information, so-called Bayesian games. He also made important contributions to the use of game theory and economic reasoning in political and moral philosophy (specifically utilitarian ethics) as well as contributing to the study of equilibrium selection. For his work, he was a co-recipient along with John Nash and Reinhard Selten of the 1994 Nobel Memorial Prize in Economic Sciences. He moved to the United States in 1956, and spent most of his life there. According to György Marx, he was one of The Martians. Early life Harsanyi was born on May 29, 1920, in Budapest, Hungary, the son of Alice H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Strategy
In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. A player's strategy will determine the action which the player will take at any stage of the game. In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines. The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibria
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pure Strategy
In game theory, a player's strategy is any of the options which they choose in a setting where the outcome depends ''not only'' on their own actions ''but'' on the actions of others. The discipline mainly concerns the action of a player in a game affecting the behavior or actions of other players. Some examples of "games" include chess, bridge, poker, monopoly, diplomacy or battleship. A player's strategy will determine the action which the player will take at any stage of the game. In studying game theory, economists enlist a more rational lens in analyzing decisions rather than the psychological or sociological perspectives taken when analyzing relationships between decisions of two or more parties in different disciplines. The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incomplete Information
In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay. Given this information, the players have the ability to plan accordingly based on the information to maximize their own strategies and utility at the end of the game. Inversely, in a game with incomplete information, players do not possess full information about their opponents. Some players possess private information, a fact that the others should take into account when forming expectations about how those players will behave. A typical example is an auction: each player knows his own utility function (valuation for the item), but does not know the utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Idealization (science Philosophy)
In philosophy of science, idealization is the process by which Scientific modelling, scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve. That is, it is determined whether the phenomenon approximates an "ideal case," then the model is applied to make a prediction based on that ideal case. If an approximation is accurate, the model will have high predictive power; for example, it is not usually necessary to account for air resistance when determining the acceleration of a falling bowling ball, and doing so would be more complicated. In this case, air resistance is idealized to be zero. Although this is not strictly true, it is a good approximation because its effect is negligible compared to that of gravity. Idealizations may allow predictions to be made when none otherwise could be. For example, the approximation of air resistance as zero was the only option before the formulation of Stokes' law al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ex-ante
The term ''ex-ante'' (sometimes written ''ex ante'' or ''exante'') is a phrase meaning "before the event". Ex-ante or notional demand refers to the desire for goods and services that is not backed by the ability to pay for those goods and services. This is also termed as 'wants of people'. ''Ex-ante'' is used most commonly in the commercial world, where results of a particular action, or series of actions, are forecast (or intended). The opposite of ''ex-ante'' is ''ex-post'' (actual) (or ''ex post''). Buying a lottery ticket loses you money ex ante (in expectation), but if you win, it was the right decision ex post. Examples: * In the financial world, the ''ex-ante return'' is the expected return of an investment portfolio. * In the recruitment industry, ''ex-ante'' is often used when forecasting resource requirements on large future projects. The ''ex-ante'' (and ''ex-post'') reasoning in economic topics was introduced mainly by Swedish economist Gunnar Myrdal in his 1927– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuum (theory)
Continuum theories or models explain variation as involving gradual quantitative transitions without abrupt changes or discontinuities. In contrast, categorical theories or models explain variation using qualitatively different states. In physics In physics, for example, the space-time continuum model describes space and time as part of the same continuum rather than as separate entities. A spectrum in physics, such as the electromagnetic spectrum, is often termed as either continuous (with energy at all wavelengths) or discrete (energy at only certain wavelengths). In contrast, quantum mechanics uses quanta, certain defined amounts (i.e. categorical amounts) which are distinguished from continuous amounts. In mathematics and philosophy A good introduction to the philosophical issues involved is John Lane Bell'essayin th''Stanford Encyclopedia of Philosophy'' A significant divide is provided by the law of excluded middle. It determines the divide between intuitionist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Information
In economics and game theory, complete information is an economic situation or game in which knowledge about other market participants or players is available to all participants. The utility functions (including risk aversion), payoffs, strategies and "types" of players are thus common knowledge. Complete information is the concept that each player in the game is aware of the sequence, strategies, and payoffs throughout gameplay. Given this information, the players have the ability to plan accordingly based on the information to maximize their own strategies and utility at the end of the game. Inversely, in a game with incomplete information, players do not possess full information about their opponents. Some players possess private information, a fact that the others should take into account when forming expectations about how those players will behave. A typical example is an auction: each player knows his own utility function (valuation for the item), but does not know the utili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evolutionary Game Theory
Evolutionary game theory (EGT) is the application of game theory to evolving populations in biology. It defines a framework of contests, strategies, and analytics into which Darwinian competition can be modelled. It originated in 1973 with John Maynard Smith and George R. Price's formalisation of contests, analysed as strategies, and the mathematical criteria that can be used to predict the results of competing strategies. Evolutionary game theory differs from classical game theory in focusing more on the dynamics of strategy change. This is influenced by the frequency of the competing strategies in the population. Evolutionary game theory has helped to explain the basis of altruistic behaviours in Darwinian evolution. It has in turn become of interest to economists, sociologists, anthropologists, and philosophers. History Classical game theory Classical non-cooperative game theory was conceived by John von Neumann to determine optimal strategies in competitions between adversa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
