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Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. 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 mathematical economics. His paper was followed by the 1944 book '' Theory of Games and Economic Behavior'', co-written with Oskar Morgenster ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cooperative Game Theory
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of Player (game), players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law). Those are opposed to non-cooperative games in which there is either no possibility to forge alliances or all agreements need to be Self-enforcing agreement, self-enforcing (e.g. through credible threats). Cooperative games are often analysed through the framework of cooperative game theory, which focuses on predicting which coalitions will form, the joint actions that groups take and the resulting collective payoffs. It is opposed to the traditional Non-cooperative game, non-cooperative game theory which focuses on predicting individual players' actions and payoffs and analyzing Nash equilibria. Cooperative game theory provides a high-level approach as it only describes the structure, strategies and payoffs of coalitions, whereas non-cooperativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
James Waldegrave, 1st Earl Waldegrave
James Waldegrave, 1st Earl Waldegrave, (168411 April 1741) was a British diplomat who served as ambassador to Austria and France. Life Waldegrave was the son of the 1st Baron Waldegrave and Henrietta FitzJames, the illegitimate daughter of James II and Arabella Churchill. Educated in France, Waldegrave inherited his father's title in 1690, and on 20 May 1714 he married Mary Webb (who died in childbirth in 1719), a daughter of Sir John Webb, 3rd Baronet and they had three surviving children: *James Waldegrave, 2nd Earl Waldegrave (1715–1763) *John Waldegrave, 3rd Earl Waldegrave (1718–1784) *Lady Henrietta Waldegrave (1717–1753), married firstly, Lord Edward Herbert, a son of the 2nd Marquess of Powis and had issue; married secondly, John Beard (a singer at Covent Garden). After the death of his wife, he converted from Roman Catholicism (the religion he was brought up in) to Anglicanism to take his seat in the House of Lords. He was briefly a Lord of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacobitism
Jacobitism (; gd, Seumasachas, ; ga, Seacaibíteachas, ) was a political movement that supported the restoration of the senior line of the House of Stuart to the Monarchy of the United Kingdom, British throne. The name derives from the first name of James II and VII, which in Latin translates as ''Jacobus (name), Jacobus''. When James went into exile after the November 1688 Glorious Revolution, the Parliament of England argued that he had abandoned the Kingdom of England, English throne, which they offered to his Protestant daughter Mary II, and her husband William III of England, William III. In April, the Convention of Estates (1689), Scottish Convention held that he "forfeited" the throne of Scotland by his actions, listed in the Articles of Grievances. The Revolution thus created the principle of a contract between monarch and people, which if violated meant the monarch could be removed. Jacobites argued monarchs were appointed by God, or Divine right of kings, divine right, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christiaan Huygens
Christiaan Huygens, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician, physicist, engineer, astronomer, and inventor, who is regarded as one of the greatest scientists of all time and a major figure in the Scientific Revolution. In physics, Huygens made groundbreaking contributions in optics and mechanics, while as an astronomer he is chiefly known for his studies of the rings of Saturn and the discovery of its moon Titan. As an engineer and inventor, he improved the design of telescopes and invented the pendulum clock, a breakthrough in timekeeping and the most accurate timekeeper for almost 300 years. An exceptionally talented mathematician and physicist, Huygens was the first to idealize a physical problem by a set of mathematical parameters, and the first to fully mathematize a mechanistic explanation of an unobservable physical phenomenon.Dijksterhuis, F.J. (2008) Stevin, Huygens and the Dutch republ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blaise Pascal
Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pascal's earliest mathematical work was on conic sections; he wrote a significant treatise on the subject of projective geometry at the age of 16. He later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social sciences, social science. In 1642, while still a teenager, he started some pioneering work on calculating machines (called Pascal's calculators and later Pascalines), establishing him as one of the first two inventors of the mechanical calculator. Like his contemporary René Descartes, Pascal was also a pioneer in the natural and applied sciences. Pascal wrote in defense of the scientific method and produced several controversial results. He made important contribu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerolamo Cardano
Gerolamo Cardano (; also Girolamo or Geronimo; french: link=no, Jérôme Cardan; la, Hieronymus Cardanus; 24 September 1501– 21 September 1576) was an Italian polymath, whose interests and proficiencies ranged through those of mathematician, physician, biologist, physicist, chemist, astrologer, astronomer, philosopher, writer, and gambler. He was one of the most influential mathematicians of the Renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficients and the binomial theorem in the Western world. He wrote more than 200 works on science. Cardano partially invented and described several mechanical devices including the combination lock, the gimbal consisting of three concentric rings allowing a supported compass or gyroscope to rotate freely, and the Cardan shaft with universal joints, which allows the transmission of rotary motion at various angles and is used in vehicles to this day. He made sig ... [...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] |
Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord. The Prize is awarded in partnership between the Royal Swedish Academy of Sciences and the Crafoord Foundation in Lund. The Academy is responsible for selecting the Crafoord Laureates. The prize is awarded in four categories: astronomy and mathematics; Geology, geosciences; Biology, biosciences, with particular emphasis on ecology; and polyarthritis, the disease from which Holger severely suffered in his last years. According to the Academy, "these disciplines are chosen so as to complement those for which the Nobel Prizes are awarded". Only one award is given each year, according to a rotating scheme – astronomy and mathematics; then geosciences; then biosciences. A Crafoord Prize in polyarthritis is only awarded when a special committee decides that substantial progress in the field has been made. The recipient of the Crafoord Prize is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Maynard Smith
John Maynard Smith (6 January 1920 – 19 April 2004) was a British theoretical and mathematical evolutionary biologist and geneticist. Originally an aeronautical engineer during the Second World War, he took a second degree in genetics under the well-known biologist J. B. S. Haldane. Maynard Smith was instrumental in the application of game theory to evolution with George R. Price, and theorised on other problems such as the evolution of sex and signalling theory. Biography Early years John Maynard Smith was born in London, the son of the surgeon Sidney Maynard Smith, but following his father's death in 1928, the family moved to Exmoor, where he became interested in natural history. Quite unhappy with the lack of formal science education at Eton College, Maynard Smith took it upon himself to develop an interest in Darwinian evolutionary theory and mathematics, after having read the work of old Etonian J. B. S. Haldane, whose books were in the school's library despite the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert B
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' ( non, Hróðr) "fame, glory, honour, praise, renown" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe it entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including English, German, Dutch, Norwegian, Swedish, Scots, Danish, and Icelandic. It can be use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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