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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 Émile 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 ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constant-sum Game
Zero-sum game is a mathematical representation in game theory and economic theory of a situation which involves two sides, 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, therefore 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, 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 all participants value each unit of cake equally. Other examples of zero-sum games in daily life include games like poker, chess, and bridge where one person gains and another person loses, which results in a zero-net benefit for every player. In the markets and financial instruments, futures contracts and options are zero-sum games as well. In c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Émile Borel
Félix Édouard Justin Émile Borel (; 7 January 1871 – 3 February 1956) was a French mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ... 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 Collège Sainte-Barbe and Lycée Louis-le-Grand before applying to both the École normale supérieure (Paris), École normale supérieure and the École 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 général, an annual national mathematics competition. After graduating in 1892, he placed first in the agrégati ... [...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] |
Nash Equilibrium
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] |
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 while serving in the Wei state and was sentenced to face-tattooing (criminal branding) and had his kneecaps removed (trad. 臏, sim. 膑, pinyin: ''bìn''), permanently crippling him. Sun escaped from Wei later and rose to prominence in the Qi state, by serving as a military strategist and commander. He led Qi to victory against the Wei state at the Battle of Guiling and Battle of Maling. Sun authored the military treatise ''Sun Bin's Art of War'', which was rediscovered in a 1972 archaeological excavation after being lost for almost 2000 years. Life Early life An alleged descendant of Sun Tzu, Sun Bin was recognized for his brilliance at an early age, while he was still studying military strategy under the tutelag ... [...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 (1790–1832), French Egyptologist * Jean-François Clervoy (born 1958), French engineer and astronaut * Jean-François Corminboeuf (born 1953), Swiss sport sailor * Jean-François Dagenais (born 1975), Canadian music producer * Jean-François David (born 1982), Canadian ice hockey player * Jean-François Gariépy (born 1984), Canadian alt-right political commentator and former neuroscientist * Jean-François Garreaud (1946–2020), French actor * Jean-François de La Harpe (1739–1803), French critic * Jean-François Lyotard (1924-1998), French philosopher * Jean-François Marceau (born 1976), Canadian judoka * Jean-François Marmontel (1723–1799), French historian and writer * Jean-François Martial (1891–1977), Belgian actor * Jean-François Millet (1814–1875), French painter * Jean-François Papillon (d ... [...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 taken ... [...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 Béla Bollobás. Career Partington works in the area of functional 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, Fyleet, Crobe, Sang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
