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Proper Equilibrium
Proper equilibrium is a refinement of Nash Equilibrium by Roger B. Myerson. Proper equilibrium further refines Reinhard Selten's notion of a trembling hand perfect equilibrium by assuming that more costly trembles are made with significantly smaller probability than less costly ones. Definition Given a normal form game and a parameter \epsilon > 0, a totally mixed strategy profile \sigma is defined to be \epsilon-proper if, whenever a player has two pure strategies s and s' such that the expected payoff of playing s is smaller than the expected payoff of playing s' (that is u(s,\sigma_) Example The game to the right is a varia ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trembling Hand Perfect Equilibrium
In game theory, trembling hand perfect equilibrium is a type of refinement of a Nash equilibrium that was first proposed by Reinhard Selten. A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or tremble, may choose unintended strategies, albeit with negligible probability. Definition First define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played. A totally mixed strategy is a mixed strategy in an n-player strategic game where ''every'' pure strategy is played with positive probability. This is the "trembling hands" of the players; they sometimes play a different strategy, other than the one they intended to play. Then define a mixed strategy profile \sigma=(\sigma_1,\ldots,\sigma_n) as being trembling hand perfect if there is a sequence of perturbed game ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roger B
Roger is a masculine given name, and a surname. The given name is derived from the Old French personal names ' and '. These names are of Germanic languages">Germanic origin, derived from the elements ', ''χrōþi'' ("fame", "renown", "honour") and ', ' ("spear", "lance") (Hrōþigēraz). The name was introduced into England by the Normans. In Normandy, the Franks, Frankish name had been reinforced by the Old Norse cognate '. The name introduced into England replaced the Old English cognate '. ''Roger'' became a very common given name during the Middle Ages. A variant form of the given name ''Roger'' that is closer to the name's origin is '' Rodger''. Slang and other uses From up to , Roger was slang for the word "penis". In ''Under Milk Wood'', Dylan Thomas writes "jolly, rodgered" suggesting both the sexual double entendre and the pirate term "Jolly Roger". In 19th-century England, Roger was slang for another term, the cloud of toxic green gas that swept through the chlori ... [...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] |
Reinhard Selten
Reinhard Justus Reginald Selten (; 5 October 1930 – 23 August 2016) was a German economics, economist, who won the 1994 Nobel Memorial Prize in Economic Sciences (shared with John Harsanyi and John Forbes Nash, John Nash). He is also well known for his work in bounded rationality and can be considered one of the founding fathers of experimental economics. Biography Selten was born in Wrocław, Breslau (Wrocław) in Province of Lower Silesia, Lower Silesia, now in Poland, to a Jewish father, Adolf Selten (a blind bookseller; d. 1942Roberts, Sam"Reinhard Selten, Whose Strides in Game Theory Led to a Nobel, Dies at 85" New York ''Times'', September 2, 2016. Retrieved 2016-09-03.), and Protestant mother, Käthe Luther.O'Connor, J J, and E F Robertson"Reinhard Selten" ''www-history.mcs.st-and.ac.uk'', November 2010. Retrieved 2016-09-03. Reinhard Selten was raised as Protestant. After a brief family exile in Saxony and Austria, Selten returned to Hesse, Germany, after the wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trembling Hand Perfect Equilibrium
In game theory, trembling hand perfect equilibrium is a type of refinement of a Nash equilibrium that was first proposed by Reinhard Selten. A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming that the players, through a "slip of the hand" or tremble, may choose unintended strategies, albeit with negligible probability. Definition First define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played. A totally mixed strategy is a mixed strategy in an n-player strategic game where ''every'' pure strategy is played with positive probability. This is the "trembling hands" of the players; they sometimes play a different strategy, other than the one they intended to play. Then define a mixed strategy profile \sigma=(\sigma_1,\ldots,\sigma_n) as being trembling hand perfect if there is a sequence of perturbed game ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Form (abstract Rewriting)
In abstract rewriting, an object is in normal form if it cannot be rewritten any further, i.e. it is irreducible. Depending on the rewriting system, an object may rewrite to several normal forms or none at all. Many properties of rewriting systems relate to normal forms. Definitions Stated formally, if (''A'',→) is an abstract rewriting system, ''x''∈''A'' is in normal form if no ''y''∈''A'' exists such that ''x''→''y'', i.e. ''x'' is an irreducible term. An object ''a'' is weakly normalizing if there exists at least one particular sequence of rewrites starting from ''a'' that eventually yields a normal form. A rewriting system has the weak normalization property or is ''(weakly) normalizing'' (WN) if every object is weakly normalizing. An object ''a'' is strongly normalizing if every sequence of rewrites starting from ''a'' eventually terminates with a normal form. A rewriting system is ''strongly normalizing'', ''terminating'', ''noetherian'', or has the (strong) norma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mixed Strategy
In game theory, a move, action, or play is any one of the options which a player can choose in a setting where the optimal 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. The term strategy is typically used to mean a complete algorithm for playing a game, telling a player what to do for every possible situation. A player's strategy determines the action the player will take at any stage of the game. However, the idea of a strategy is often confused or conflated with that of a move or action, because of the correspondence between moves and pure strategies in most games: for any move ''X'', "always play move ''X''" is an example of a valid strategy, and as a result every move can also be considered to be a strategy. Other authors treat strate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matching Pennies
Matching pennies is a non-cooperative game studied in game theory. It is played between two players, Even and Odd. Each player has a penny and must secretly turn the penny to heads or tails. The players then reveal their choices simultaneously. If the pennies match (both heads or both tails), then Even wins and keeps both pennies. If the pennies do not match (one heads and one tails), then Odd wins and keeps both pennies. Theory Matching Pennies is a zero-sum game because each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the participants' total gains are added up and their total losses subtracted, the sum will be zero. The game can be written in a payoff matrix (pictured right - from Even's point of view). Each cell of the matrix shows the two players' payoffs, with Even's payoffs listed first. Matching pennies is used primarily to illustrate the concept of mixed strategies and a mixed str ... [...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] |
Extensive Form Game
In game theory, an extensive-form game is a specification of a game allowing for the explicit representation of a number of key aspects, like the sequencing of players' possible moves, their choices at every decision point, the (possibly imperfect) information each player has about the other player's moves when they make a decision, and their payoffs for all possible game outcomes. Extensive-form games also allow for the representation of incomplete information in the form of chance events modeled as " moves by nature". Extensive-form representations differ from normal-form in that they provide a more complete description of the game in question, whereas normal-form simply boils down the game into a payoff matrix. Finite extensive-form games Some authors, particularly in introductory textbooks, initially define the extensive-form game as being just a game tree with payoffs (no imperfect or incomplete information), and add the other elements in subsequent chapters as refinements ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasi-perfect Equilibrium
Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. Informally, a player playing by a strategy from a quasi-perfect equilibrium takes observed as well as potential future mistakes of his opponents into account but assumes that he himself will not make a mistake in the future, even if he observes that he has done so in the past. Quasi-perfect equilibrium is a further refinement of sequential equilibrium. It is itself refined by normal form proper equilibrium. Mertens' voting game It has been argued by Jean-François MertensJean-François Mertens. "Two examples of strategic equilibrium." ''Games and Economic Behavior'', 8:378--388, 1995. that quasi-perfect equilibrium is superior to Reinhard Selten Reinhard Justus Reginald Selten (; 5 October 1930 – 23 August 2016) was a German economics, economist, who won the 1994 Nobel Memorial Prize in Economic Sciences (shared with John Harsanyi and John Forbes Nash, J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric Van Damme
Eric Eleterius Coralie van Damme (born 27 July 1956CURRICULUM VITAE Eric van Damme version: 17 April 2013) is a Dutch and Professor of Economics at the , known for his contributions to . Biography Born in , Van Damme received his MA in Mathemat ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
