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Information Set (game Theory)
In game theory, an information set is a set that, for a particular player, given what that player has observed shows the decision vertices available to the player which are undistinguishable to them at the current point in the game. For a better idea on decision vertices, refer to Figure 1. If the game has perfect information, every information set contains only one member, namely the point actually reached at that stage of the game, since each player knows the exact mix of chance moves and player strategies up to the current point in the game. Otherwise, it is the case that some players cannot be sure exactly what has taken place so far in the game and what their position is. Information sets are used in extensive form games and are often depicted in game trees. Game trees show the path from the start of a game and the subsequent paths that can be made depending on each player's next move. Information sets can be easily depicted in game trees to display each player's possible move ... [...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] |
Battle Of The Sexes - Imperfect Information
A battle is an occurrence of combat in warfare between opposing military units of any number or size. A war usually consists of multiple battles. In general, a battle is a military engagement that is well defined in duration, area, and force commitment. An engagement with only limited commitment between the forces and without decisive results is sometimes called a skirmish. The word "battle" can also be used infrequently to refer to an entire operational campaign, although this usage greatly diverges from its conventional or customary meaning. Generally, the word "battle" is used for such campaigns if referring to a protracted combat encounter in which either one or both of the combatants had the same methods, resources, and strategic objectives throughout the encounter. Some prominent examples of this would be the Battle of the Atlantic, Battle of Britain, and Battle of Stalingrad, all in World War II. Wars and military campaigns are guided by military strategy, whereas bat ... [...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 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] |
Simultaneous Game
In game theory, a simultaneous game or static game is a game where each player chooses their action without knowledge of the actions chosen by other players. Simultaneous games contrast with sequential games, which are played by the players taking turns (moves alternate between players). In other words, both players normally act at the same time in a simultaneous game. Even if the players do not act at the same time, both players are uninformed of each other's move while making their decisions. Normal form representations are usually used for simultaneous games.Mailath, G., Samuelson, L. and Swinkels, J., 1993. Extensive Form Reasoning in Normal Form Games. Econometrica, nline61(2), pp.273-278. Available at: ccessed 30 October 2020 Given a continuous game, players will have different information sets if the game is simultaneous than if it is sequential because they have less information to act on at each step in the game. For example, in a two player continuous game that is se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgame Perfect Equilibrium
In game theory, a subgame perfect equilibrium (or subgame perfect Nash equilibrium) is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game. Informally, this means that at any point in the game, the players' behavior from that point onward should represent a Nash equilibrium of the continuation game (i.e. of the subgame), no matter what happened before. Every finite extensive game with perfect recall has a subgame perfect equilibrium. Perfect recall is a term introduced by Harold W. Kuhn in 1953 and ''"equivalent to the assertion that each player is allowed by the rules of the game to remember everything he knew at previous moves and all of his choices at those moves"''. A common method for determining subgame perfect equilibria in the case of a finite game is backward induction. Here one first considers the last actions of the game and determ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal-form Game
In game theory, normal form is a description of a ''game''. Unlike extensive form, normal-form representations are not graphical ''per se'', but rather represent the game by way of a matrix. While this approach can be of greater use in identifying strictly dominated strategies and Nash equilibria, some information is lost as compared to extensive-form representations. The normal-form representation of a game includes all perceptible and conceivable strategies, and their corresponding payoffs, for each player. In static games of complete, perfect information, a normal-form representation of a game is a specification of players' strategy spaces and payoff functions. A strategy space for a player is the set of all strategies available to that player, whereas a strategy is a complete plan of action for every stage of the game, regardless of whether that stage actually arises in play. A payoff function for a player is a mapping from the cross-product of players' strategy spaces to that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Battle Of The Sexes (game Theory)
In game theory, the battle of the sexes is a two-player coordination game that also involves elements of conflict. The game was introduced in 1957 by R. Duncan Luce and Howard Raiffa in their classic book, ''Games and Decisions''. Some authors prefer to avoid assigning sexes to the players and instead use Players 1 and 2, and some refer to the game as Bach or Stravinsky, using two concerts as the two events. The game description here follows Luce and Raiffa's original story. Imagine that a man and a woman hope to meet this evening, but have a choice between two events to attend: a prize fight and a ballet. The man would prefer to go to prize fight. The woman would prefer the ballet. Both would prefer to go to the same event rather than different ones. If they cannot communicate, where should they go? The payoff matrix labeled "Battle of the Sexes (1)" shows the payoffs when the man chooses a row and the woman chooses a column. In each cell, the first number represents the ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Battle Of The Sexes - Perfect Information
A battle is an occurrence of combat in warfare between opposing military units of any number or size. A war usually consists of multiple battles. In general, a battle is a military engagement that is well defined in duration, area, and force commitment. An engagement with only limited commitment between the forces and without decisive results is sometimes called a skirmish. The word "battle" can also be used infrequently to refer to an entire operational campaign, although this usage greatly diverges from its conventional or customary meaning. Generally, the word "battle" is used for such campaigns if referring to a protracted combat encounter in which either one or both of the combatants had the same methods, resources, and strategic objectives throughout the encounter. Some prominent examples of this would be the Battle of the Atlantic, Battle of Britain, and Battle of Stalingrad, all in World War II. Wars and military campaigns are guided by military strategy, whereas bat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Information
In economics, perfect information (sometimes referred to as "no hidden information") is a feature of perfect competition. With perfect information in a market, all consumers and producers have complete and instantaneous knowledge of all market prices, their own utility, and own cost functions. In game theory, a sequential game has perfect information if each player, when making any decision, is perfectly informed of all the events that have previously occurred, including the "initialization event" of the game (e.g. the starting hands of each player in a card game).Archived aGhostarchiveand thWayback Machine Perfect information defined at 0:25, with academic sources and . Perfect information is importantly different from complete information, which implies common knowledge of each player's utility functions, payoffs, strategies and "types". A game with perfect information may or may not have complete information. Games where some aspect of play is ''hidden'' from opponents - su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poker
Poker is a family of comparing card games in which players wager over which hand is best according to that specific game's rules. It is played worldwide, however in some places the rules may vary. While the earliest known form of the game was played with just 20 cards, today it is usually played with a standard deck, although in countries where short packs are common, it may be played with 32, 40 or 48 cards.Parlett (2008), pp. 568–570. Thus poker games vary in deck configuration, the number of cards in play, the number dealt face up or face down, and the number shared by all players, but all have rules that involve one or more rounds of betting. In most modern poker games, the first round of betting begins with one or more of the players making some form of a forced bet (the '' blind'' or ''ante''). In standard poker, each player bets according to the rank they believe their hand is worth as compared to the other players. The action then proceeds clockwise as each play ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest coverage of any mathematician of his time and was said to have been "the last representative of the great mathematicians who were equally at home in both pure and applied mathematics". He integrated pure and applied sciences. Von Neumann made major contributions to many fields, including mathematics (foundations of mathematics, measure theory, functional analysis, ergodic theory, group theory, lattice theory, representation theory, operator algebras, matrix theory, geometry, and numerical analysis), physics (quantum mechanics, hydrodynamics, ballistics, nuclear physics and quantum statistical mechanics), economics ( game theory and general equilibrium theory), computing ( Von Neumann architecture, linear programming, numerical meteo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
