This link has been bookmarked by 94 people . It was first bookmarked on 06 Aug 2006, by bkh.
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29 Aug 15
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26 Oct 14
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each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy
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no player can benefit by changing strategies while the other players keep theirs unchanged
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"an equilibrium point is an n-tuple such that each player's mixed strategy maximizes his payoff if the strategies of the others are held fixed. Thus each player's strategy is optimal against those of the others."
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a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy
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every player
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is indifferent between switching and not
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Thus, each strategy in a Nash equilibrium is a best response to all other strategies in that equilibrium
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then the set of strategies is a Nash equilibrium
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and
be a strategy profile of all players except for player 
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where
is the strategy set for player , -
strictly (with > instead of ≥)
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strict Nash equilibrium
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if we allow mixed strategies, then every game with a finite number of players in which each player can choose from finitely many pure strategies has at least one Nash equilibrium
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- who did not change has no better strategy in the new circumstance
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who did change is now playing with a strictly worse strategy
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then a player with the small change in his mixed-strategy will return immediately to the Nash equilibrium. The equilibrium is said to be stable.
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If either player changes his probabilities, then the other player immediately has a better strategy at either (0%, 100%) or (100%, 0%).
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unilateral deviations
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17 Jun 14
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04 May 14
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01 Mar 14
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In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.[1]:14 If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, Amy and Wili are in Nash equilibrium if Amy is making the best decision she can, taking into account Wili's decision, and Wili is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others.
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23 Feb 14
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26 Dec 13
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19 Jul 13
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In game theory, the Nash equilibrium is a solution concept of a non-cooperative game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy unilaterally.[1]:14 If each player has chosen a strategy and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, Amy and Wili are in Nash equilibrium if Amy is making the best decision she can, taking into account Wili's decision, and Wili is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others.
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02 Jan 13
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24 Nov 12
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There is common knowledge that all players meet these conditions, including this one. So, not only must each player know the other players meet the conditions, but also they must know that they all know that they meet them, and know that they know that they know that they meet them, and so on.
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The payoff in economics is utility (or sometimes money), and in evolutionary biology gene transmission, both are the fundamental bottom line of surviva
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27 Oct 12
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22 Oct 12
avichosvjikgood overview
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11 Oct 12
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02 Oct 12
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In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally.[1]:14 If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision. Likewise, a group of players are in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others.
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30 Sep 12
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23 Jul 12
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o player has anything to gain by changing only his own strategy unilaterally.
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03 Apr 12
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03 Oct 11
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predicting what will happen if several people or several institutions are making decisions at the same time, and if the outcome depends on the decisions of the others.
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23 Jul 11
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08 Jul 11
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22 Jun 11
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equilibrium
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unilaterally
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Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision
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13 Jun 11
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Nash equilibrium
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In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally.
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If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.
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Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision. Likewise, a group of players is in Nash equilibrium if each one is making the best decision that he or she can, taking into account the decisions of the others.
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Nash equilibrium does not necessarily mean the best payoff for all the players involved
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21 Apr 11
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16 Dec 10
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no player has anything to gain by changing only his or her own strategy unilaterally
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09 Jul 10
shaida ghomashchiRonald David Laing (7 October 1927 – 23 August 1989), was a Scottish psychiatrist who wrote extensively on mental illness – in particular, the experience of psychosis. Laing's views on the causes and treatment of serious mental dysfunction, greatly influenced by existential philosophy, ran counter to the psychiatric orthodoxy of the day by taking the expressed feelings of the individual patient or client as valid descriptions of lived experience rather than simply as symptoms of some separate or underlying disorder. Often associated with the anti-psychiatry movement, he himself rejected the label as such, as did certain others critical of conventional psychiatry at the time
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In game theory, Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his or her own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium
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01 Jun 10
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Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision.
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The simple insight underlying John Nash's idea is that we cannot predict the result of the choices of multiple decision makers if we analyze those decisions in isolation.
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22 May 10
elvis krantNash Equilibrium In game theory Nash equilibrium (named after John Forbes Nash , who proposed it) is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, a
Adjusted Winner procedure All-pay auction Ariel Rubinstein Arms race Arrow's impossibility theorem Backward induction Bargaining Problem Nash equilibrium Wikipedia articles needing factual verification since July 2007
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16 May 10
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The contribution of John Forbes Nash in his 1951 article Non-Cooperative Games was to define a mixed strategy Nash Equilibrium for any game with a finite set of actions and prove that at least one (mixed strategy) Nash Equilibrium must exist.
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04 Feb 10
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22 Dec 09
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06 Oct 09
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25 Aug 09
Patrick HelmesFrom game theory, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy
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22 Jan 09
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11 Nov 08
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14 Aug 08
Michel BauwensAmy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision. Likewise, many players are in Nash equilibrium if each o
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30 May 08
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Nash equilibrium
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Knowing the strategies of the other players, and treating the strategies of the other players as set in stone, can I benefit by changing my strategy?
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Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved; in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium. For example, even though all depositors are hurt when a bank run occurs, it is not clear that there is any way depositors could coordinate to prevent the run.
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in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium (eg. competing businessmen forming a cartel in order to increase their profits)
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mixed-strategies, where players choose a probability distribution over possible actions
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29 May 08
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30 Apr 08
Curtis KentIn game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which no player has anything to gain by changing only his or her own strategy unilaterally.
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27 Mar 08
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30 Nov 07
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02 Sep 07
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31 May 07
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Stability
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Occurrence
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Nash equilibrium
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24 Apr 07
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The globally optimal strategy is unstable; it is not an equilibrium.
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- the player who did not change has no better strategy in the new circumstance
- the player who did change is now playing with a strictly worse strategy
A Nash equilibrium for a mixed strategy game is stable if a small change (specifically, an infinitesimal change) in probabilities for one player leads to a situation where two conditions hold:
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21 May 06
be a strategy profile of all players except for player 
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is the strategy set for player 
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