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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] |
Sequential Equilibrium
Sequential equilibrium is a refinement of Nash equilibrium for extensive form games due to David M. Kreps and Robert Wilson. A sequential equilibrium specifies not only a strategy for each of the players but also a ''belief'' for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on the nodes in the information set. A profile of strategies and beliefs is called an ''assessment'' for the game. Informally speaking, an assessment is a perfect Bayesian equilibrium if its strategies are sensible given its beliefs ''and'' its beliefs are confirmed on the outcome path given by its strategies. The definition of sequential equilibrium further requires that there be arbitrarily small perturbations of beliefs and associated strategies with the same property. Consistent assessments The formal definition of a strategy being sensible given a belief is straightforward; the strategy should simply maximize expec ... [...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] |
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] |
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] |
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] |
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Equilibrium
Sequential equilibrium is a refinement of Nash equilibrium for extensive form games due to David M. Kreps and Robert Wilson. A sequential equilibrium specifies not only a strategy for each of the players but also a ''belief'' for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on the nodes in the information set. A profile of strategies and beliefs is called an ''assessment'' for the game. Informally speaking, an assessment is a perfect Bayesian equilibrium if its strategies are sensible given its beliefs ''and'' its beliefs are confirmed on the outcome path given by its strategies. The definition of sequential equilibrium further requires that there be arbitrarily small perturbations of beliefs and associated strategies with the same property. Consistent assessments The formal definition of a strategy being sensible given a belief is straightforward; the strategy should simply maximize expec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Jean-François Mertens
Jean-François Mertens (11 March 1946 – 17 July 2012) was a Belgian game theorist and mathematical economist. Mertens contributed to economic theory in regards to order-book of market games, cooperative games, noncooperative games, repeated games, epistemic models of strategic behavior, and refinements of Nash equilibrium (see solution concept). In cooperative game theory he contributed to the solution concepts called the core and the Shapley value. Regarding repeated games and stochastic games, Mertens 1982 and 1986 survey articles, and his 1994 survey co-authored with Sylvain Sorin and Shmuel Zamir, are compendiums of results on this topic, including his own contributions. Mertens also made contributions to probability theory and published articles on elementary topology. Epistemic models Mertens and Zamir implemented John Harsanyi's proposal to model games with incomplete information by supposing that each player is characterized by a privately known type that describes h ... [...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] |
