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Blotto Game
A Colonel Blotto game is a type of two-person constant-sum game in which the players (officers) are tasked to simultaneously distribute limited resources over several objects (battlefields). In the classic version of the game, the player devoting the most resources to a battlefield wins that battlefield, and the gain (or payoff) is equal to the total number of battlefields won. The game was first proposed by Ămile Borel in 1921. In 1938 Borel and Ville published a particular optimal strategy (the "disk" solution). The game was studied after the Second World War by scholars in Operation Research, and became a classic in game theory. Gross and Wagner's 1950 research memorandum states Borel's optimal strategy, and coined the fictitious Colonel Blotto and Enemy names. For three battlefields or more, the space of pure strategies is multi-dimensional (two dimensions for three battlefields) and a mixed strategy is thus a probability distribution over a continuous set. The game is a rare ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant-sum Game
Zero-sum game is a Mathematical model, mathematical representation in game theory and economic theory of a situation that involves two competition, competing entities, where the result is an advantage for one side and an equivalent loss for the other. In other words, player one's gain is equivalent to player two's loss, with the result that the net improvement in benefit of the game is zero. If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus, Fair cake-cutting, cutting a cake, where taking a more significant piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if marginal utility, all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, sport and Contract bridge, bridge where one person gains and another person loses, which results in a zero-net benefit for every ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ămile Borel
FĂ©lix Ădouard Justin Ămile Borel (; 7 January 1871 â 3 February 1956) was a French people, French mathematician and politician. As a mathematician, he was known for his founding work in the areas of measure theory and probability. Biography Borel was born in Saint-Affrique, Aveyron, the son of a Protestant pastor. He studied at the CollĂšge Sainte-Barbe and LycĂ©e Louis-le-Grand before applying to both the Ăcole normale supĂ©rieure (Paris), Ăcole normale supĂ©rieure and the Ăcole Polytechnique. He qualified in the first position for both and chose to attend the former institution in 1889. That year he also won the concours gĂ©nĂ©ral, an annual national mathematics competition. After graduating in 1892, he placed first in the agrĂ©gation, a competitive civil service examination leading to the position of professeur agrĂ©gĂ©. His thesis, published in 1893, was titled ''Sur quelques points de la thĂ©orie des fonctions'' ("On some points in the theory of functions"). That y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games 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 f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium is the most commonly used solution concept for non-cooperative games. A Nash equilibrium is a situation where no player could gain by changing their own strategy (holding all other players' strategies fixed). The idea of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to his model of competition in an oligopoly. 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 theirs 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 has no other strategy available that does better than B at maximizing his payoff in response to Alice c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sun Bin
Sun Bin (died 316 BC) was a Chinese general, military strategist, and writer who lived during the Warring States period of Chinese history. A supposed descendant of Sun Tzu, Sun was tutored in military strategy by the hermit Guiguzi. He was accused of treason by Pang Juan while serving Wei and punished by being branded and crippled. Sun escaped and became a strategist and commander for Qi, defeating Wei at the Battle of Guiling and the Battle of Maling; Pang was killed at Maling. Sun's '' Art of War'' with the Yinqueshan Han Slips were discovered in 1972 after going missing for at least 1400 years. Life Early life and service in Wei Sun Bin was allegedly a descendant of Sun Tzu. Sun Bin excelled while studying military strategy under the hermit Guiguzi; he could recite ''The Art of War'' and identified by Guiguzi as a role model for other students. Pang Juan, a fellow student, became Sun's blood brother. Pang left to be a Wei general, and built a reputation throu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tian Ji
Tian Ji (), courtesy name Qi (éœ), was a military general of the Qi (state), Qi state during the early Warring States period (4th century BC) of History of China, Chinese history. Tian Ji met Sun Bin and recommended him to King Wei of Qi as a military strategist. Tian Ji commanded the Qi armies in the Battle of Guiling and Battle of Maling, scoring victories against the Wei (state), Wei state with help and guidance from Sun Bin. Biography Tian Ji was descended from an aristocratic clan based in the State of Qi and was later appointed a military general by King Wei of Qi. In 340 BC, Sun Bin arrived in the State of Qi as a refugee from the State of Wei. Tian Ji met Sun Bin and was so impressed with Sun's expertise in military strategy that he kept Sun at his residence as a Retainers in early China (social group), retainer (éšćźą). Once, Tian Ji was invited to participate in a horse-racing event hosted by the king and Sun Bin proposed a strategy for Tian Ji to win. Tian used his in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-François Laslier
Jean-François () is a French given name. Notable people bearing the given name include: * Jean-François Carenco (born 1952), French politician * Jean-François Champollion (1790â1832), French Egyptologist * Jean-François Clervoy (born 1958), French engineer and astronaut * Jean-François Corminboeuf (born 1953), Swiss sport sailor * Jean-François Coulomme (born 1966), French politician * Jean-François Dagenais (born 1975), Canadian music producer * Jean-François David (born 1982), Canadian ice hockey player * Jean-François GariĂ©py (born 1984), Canadian alt-right political commentator and former neuroscientist * Jean-François Garreaud (1946â2020), French actor * Jean-François de La Harpe (1739â1803), French critic * Jean-François Larose (born 1972), Canadian politician * Jean-François Lyotard (1924â1998), French philosopher * Jean-François Marceau (born 1976), Canadian judoka * Jean-François Marmontel (1723â1799), French historian and writer * Jean-Franço ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Goofspiel
Goofspiel (also known as The Game of Pure Strategy, GOPS or Psychological Jujitsu) is a card game for two or more players. It was invented by Merrill Flood while at Princeton University in the 1930s, and Alex Randolph describes a similar game as having been popular with the 5th Indian Army during the Second World War. The game is simple to learn and play, but has some degree of strategic depth. It is commonly used as an example of multi-stage simultaneous move game in game theory and artificial intelligence. Game play Goofspiel is played using cards from a standard deck of cards, and is typically a two-player game, although more players are possible."GOPS" iThe Very Best Two Player Card Games ''PlayingCardDecks'', 5 October 2021. Retrieved 13 October 2021. Each suit is ranked A (low), 2, ..., 10, J, Q, K (high). One suit is singled out as the "prizes"; each of the remaining suits becomes a hand for one player, with one suit discarded if there are only two players, or take ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jonathan Partington
Jonathan Richard Partington (born 4 February 1955) is an English mathematician who is Emeritus Professor of pure mathematics at the University of Leeds. Education Professor Partington was educated at Gresham's School, Holt, and Trinity College, Cambridge, where he completed his PhD thesis entitled "Numerical ranges and the Geometry of Banach Spaces" under the supervision of BĂ©la BollobĂĄs. Career Partington works in the area of operator theory and complex analysis, sometimes applied to control theory, and is the author of several books in this area. He was formerly editor-in-chief of the ''Journal of the London Mathematical Society'', a position he held jointly with his Leeds colleague John Truss. Partington's extra-mathematical activities include the invention of thMarch March march an annual walk starting at March, Cambridgeshire. He is also known as a writer or co-writer of some of the earliest British text-based computer games, including Acheton, Hamil, Murdac, Avon, F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
