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Topic: Nash equilibrium

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  NationMaster - Encyclopedia: Nash equilibrium
In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally.
Nash equilibrium · Subgame perfection · Bayes-Nash ;· Trembling hand · Proper equilibrium · Epsilon-equilibrium ;· Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy ;· Risk dominance Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game.
A Nash Equilibrium is a set of mixed strategies for finite, non-cooperative games between two or more players whereby no player can improve his or her payoff by changing their strategy.
www.nationmaster.com /encyclopedia/Nash-equilibrium   (5782 words)

 Nash Equilibrium
Other academic theorists used the concept of 'equilibrium' in the 19th century (Maxwell, Walrus, Gibbs), for chemical and economic equilibrium in the early stages of the 20th century (van der Waals, Onnes, Keynes) before Nash used it in the middle of the 20th century.
As in a contemporary neo-Darwinian scientific notion of Nash Equilibrium, the gaming concepts of 'competition' and 'survival,' may be psychologically associated with the ideas of (non)'cooperation' and of 'aid' (Kroptokin), or with other conflict paradigms theorized in the human and/or social sciences.
Equilibrium theory struggles to satisfy academic standards in contemporary social sciences (and economics), which require a double hermeneutical approach (Radder, 2003) in addition to the explanatory method given by the mathematical sciences, by neo-classical economics, and even in the new technological sciences.
www.iscid.org /encyclopedia/Nash_Equilibrium   (1153 words)

 Nash Equilibrium
The concept we need is called the Nash Equilibrium, after Nobel Laureate (in economics) and mathematician John Nash.
The Nash Equilibrium conception was one of these, and is probably the most widely used "solution concept" in game theory.
DEFINITION: Nash Equilibrium If there is a set of strategies with the property that no player can benefit by changing her strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute the Nash Equilibrium.
william-king.www.drexel.edu /top/eco/game/nash.html   (702 words)

 John Nash: Genius, Nobel and Schizophrenia
The Phantom was John Nash, one of the most brilliant mathematicians of his generation, who had spiraled into schizophrenia in the 1950s.
His main result, the "Nash Equilibrium", was published in 1950 in the Proceedings of the National Academy of Sciences.
Nash shared the Nobel prize in 1994 with John C. Harsanyi and Reinhard Selten - for what he claims was his "most trivial work".
www.dickran.net /nobel/nash.html   (898 words)

 PNAS Classics -- Game Theory
Nash believed that the right approach was to focus on individual decision-making, because choosing to join a coalition can simply be considered as one of the potential strategies at a player's disposal.
For such a game, Nash defined an equilibrium to be a set of strategies, one for each player, such that no player would benefit from unilaterally changing his strategy while the other players stick to their equilibrium strategies.
Nash's fellow student and current Academy Member David Gale, however, was impressed by Nash's work and urged him to "plant a flag" by publishing his proof as quickly as possible in PNAS.
www.pnas.org /misc/classics5.shtml   (2554 words)

 Nash Equilibrium and Dominant Strategies- Game Theory - Fundamental Finance
Nash Equilibrium is a term used in game theory to describe an equilibrium where each player's strategy is optimal given the strategies of all other players.
Nash Equilibria are self-enforcing; when players are at a Nash Equilibrium they have no desire to move because they will be worse off.
The Nash Equilibria are (A,a), (B,b), and (C,c).
economics.fundamentalfinance.com /game-theory/nash-equilibrium.php   (675 words)

 The Prize in Economics 1994 - Press Release
In a Nash equilibrium, all of the players' expectations are fulfilled and their chosen strategies are optimal.
Nash proposed two interpretations of the equilibrium concept: one based on rationality and the other on statistical populations.
Since the rationalistic interpretation of Nash equilibrium is based on the assumption that the players know each others' preferences, no methods had been available for analyzing games with incomplete information, despite the fact that such games best reflect many strategic interactions in the real world.
nobelprize.org /nobel_prizes/economics/laureates/1994/press.html   (2238 words)

 [No title]
A Nash equilibrium, named after John Nash, is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action.
Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy.
A Nash equilibrium may not be stable against joint action by several people; that is one of the problems with using it to define the solution to a many-person game.
www.lycos.com /info/nash-equilibrium.html   (598 words)

 Game Theory
A " Nash Equilibrium" will be reached when each agent's actions begets a reaction by all the other agents which, in turn, begets the same initial action.
In 1950, John Nash introduced the concept of a "Nash Equilibrium" (NE), which became the organizing concept under Game Theory -- even though the concept actually stretched as far back as Cournot (1838).
Nash followed this up in 1951 with the concept of a "Nash Bargaining Solution" (NBS) for coalitional games.
cepa.newschool.edu /het/schools/game.htm   (1057 words)

 PlanetMath: Nash equilibrium
A Nash equilibrium of a game is a set of (possibly mixed) strategies
Translated, this says that if any player plays any strategy other than the one in the Nash equilibrium then that player would do worse than playing the Nash equilibrium.
This is version 5 of Nash equilibrium, born on 2002-07-24, modified 2002-09-30.
planetmath.org /encyclopedia/NashEquilibrium.html   (74 words)

 Sample Chapter for Nash, J.; Kuhn, H.W. and Nasar, S., eds.: The Essential John Nash.
Yet, before Nash, economists assumed that the outcome of a two-way bargaining was determined by psychology and was therefore outside the realm of economics.
Nash’s theory of games—especially his notion of equilibrium for such games (now known as Nash equilibrium)—significantly extended the boundaries of economics as a discipline.
That is, if the predicted behavior doesn’t satisfy the condition for Nash equilibrium, then there must be at least one individual who could achieve a better outcome if she were simply made aware of her own best interests.
press.princeton.edu /chapters/i7238.html   (4380 words)

 SFB 504 glossary: (Strategic) Equilibrium
As a strategic equilibrium is a profile of strategies that is unilaterally unimprovable given that all (other) players conform to their equilibrium strategies, the concept is weak and very general, but on the other hand most games possess several strategic equilibria.
Nash equilibrium is the pure form of the basic concept of strategic equilibrium; as such, it is useful mainly in normal form games with complete information.
When allowing for randomized strategies, at least one Nash equilibrium exists in any game(unless the players' payoff functions are irregular); for an example, see the game of matching pennies in the entry on game theory.
www.sfb504.uni-mannheim.de /glossary/strateq.htm   (1206 words)

 [No title]
The structural Quantal Response Equilibrium (QRE) generalizes the Nash equilibrium by augmenting payoffs with random elements that are not removed in some limit.
Nash proved that idealized opponents will eventually play a single best strategy in any game-it's what he won the Nobel Prize for.
The mixed strategy equilibrium of the matching pennies game is well known: each player should randomize 50-50 between the two alternatives.
www.lycos.com /info/nash-equilibrium--games.html   (608 words)

 American Experience | A Brilliant Madness | Special Features
John Nash treated the more general and realistic case of a mixture of common interests and rivalry and any number of players.
Nash used novel mathematical techniques to prove the existence of equilibrium in a very general class of games.
John Nash played an important role in interpreting the first experimental study of the prisoner's dilemma, which was conducted at the Rand Corporation in 1950.
www.pbs.org /wgbh/amex/nash/sfeature/sf_dixit.html   (1987 words)

 Nash Equilibrium - Activity
Nash's ideas, therefore, are purely in the realm of the application of mathematical ideas to a bargaining problem.
The definition of a Nash equilibrium is a point where no player can improve their position by selecting any other available strategy whilst others are also playing their best option and not changing their strategies.
Nash's work in the field has been recognised as ground-breaking and it opened up the field for application to a wide range of areas, including the biological sciences.
www.bized.co.uk /educators/16-19/economics/macrocont/activity/gametheory3.htm   (1303 words)

 Nash equilibrium - Wikipedia, the free encyclopedia
In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally.
Nash proved that, if we allow mixed strategies (players choose strategies randomly according to pre-assigned probabilities), then every n-player game in which every player can choose from finitely many strategies admits at least one Nash equilibrium.
If a game has a unique Nash equilibrium and is played among players with certain characteristics, then it is true (by definition of these characteristics) that the NE strategy set will be adopted.
en.wikipedia.org /wiki/Nash_equilibrium   (2232 words)

 Game Theory Applied to Economics
Nash equilibria (solutions) are the most stable (it is where the system "settles down", to borrow from Chaos Theory) – but they are not guaranteed to be the most desirable.
Thus, the Nash equilibrium is applicable to games that are repeated and wherein each agent reacts to the acts of other agents.
Nash proved that there is an allocation of possible utility functions to these agents so that the equilibrium strategy for each one of them will be this kind of threat.
samvak.tripod.com /nm056.html   (3866 words)

 Subgame perfect equilibrium - Wikipedia, the free encyclopedia
A strategy is a subgame perfect Nash equilibrium if it leads to the optimal outcome for every player based on a given strategy for all other players at each "sub-game" position.
A common example of the use of nodes and subgame perfect Nash equilibrium is in the estimate of optimal American option exercise through a decision lattice such as a binomial tree.
The subgame perfect Nash equilibrium is normally deduced by "backward induction" from the various ultimate outcomes of the game, eliminating branches which would involve any player making a move that is not credible (optimal) from that node.
en.wikipedia.org /wiki/Subgame-perfect_Nash_equilibrium   (687 words)

 Computational Complexity: The Complexity of the Nash Equilibrium
Nash proved that for all A and B there are probability distributions σ on the rows and τ on the columns so that if the player I plays according to σ and player II plays according to τ
Using linear programming we can find Nash Equilibrium in a zero-sum game (A(i,j)=-B(i,j) for all i,j) or if we know the set of i where σ(i)=0 and the j where τ(j)=0.
For two player games it is known that there exists a "nice" Nash equilibrium (rationals with polynomially bounded numerator and denominator).
weblog.fortnow.com /2005/02/complexity-of-nash-equilibrium.html   (1126 words)

 Chapters of The Mathematics of Nash Equilibrium   (Site not responding. Last check: 2007-11-01)
The Mathematics of Nash Equilibrium is the tentative title of a project that is currently envisaged as consisting of two books.
The second considers Nash equilibrium from the point of view of semi-algebraic geometry, and presents recent results related to the computational complexity of the problem of computing all Nash equilibrium.
Taking a historical approach, the development of the theory of refinements of Nash equilibrium is intertwined with an exposition of advanced material from the theory of fixed points.
www.econ.umn.edu /~mclennan/Classes/Ec8117-8/MathNash/book.shtml   (263 words)

 John Forbes Nash and Game Theory   (Site not responding. Last check: 2007-11-01)
John Forbes Nash was born June 13, 1928 in the small city of Bluefield, West Virginia to John Nash Sr., an electrical engineer, and Margaret Virginia Martin, who had been a schoolteacher before she was married.
Nash met a woman named Eleanor Stier, and in 1953, she gave birth to his son, John David Stier.
Therefore, “both cooperate” is not an equilibrium, but “both defect” is. It should be noted that mutual defection is not only an equilibrium but also a “dominant strategy”;.
members.tripod.com /math2005uts/nash.html   (2126 words)

 John Forbes Nash - Wikipedia, the free encyclopedia
On June 13, 1928, John Forbes Nash was born in the small Appalachian city of Bluefield, West Virginia, the son of John Nash Sr., an electrical engineer and graduate of Texas AandM University, and Virginia Martin, a teacher.
Nash's recent work involves ventures in advanced game theory including partial agency which show that, as in his early career, he prefers to select his own path and problems.
It is loosely based on Sylvia Nasar's biography of the same name, and has been criticized for its inaccurate portrayal of Nash's life and schizophrenia as well as for the over-simplified representation of the famous Nash equilibrium.
en.wikipedia.org /wiki/John_Forbes_Nash   (1779 words)

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