# Nash Equilibrium

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 his 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.

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.

### Other articles related to "nash equilibrium, equilibrium, nash":

Nash Equilibrium - Computing Nash Equilibria - Examples
... To compute the mixed strategy Nash equilibrium, assign A the probability p of playing H and (1−p) of playing T, and assign B the probability q of playing H and (1−q) of playing T ... + (+1)(1−p) = 1−2p E = E ⇒ 2p−1 = 1−2p ⇒ p = 1/2 Thus a mixed strategy Nash equilibrium in this game is for each player to randomly choose H or T with equal probability ...
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 ... game that consisted of only one part of the larger game and (2) their behavior represents a Nash equilibrium of that smaller game, then their behavior is a subgame perfect equilibrium of the larger game ...
Traveler's Dilemma
... the traveler's optimum choice (in terms of Nash equilibrium) is in fact \$2 that is, the traveler values the antiques at the airline manager's minimum allowed price ... rewarded by deviating strongly from the Nash equilibrium in the game and obtain much higher rewards than would be realized with the purely rational strategy ... deletion of dominated strategies in order to demonstrate the Nash equilibrium, and that both lead to experimental results that deviate markedly from the game-theoretical predictions ...
Strategic Dominance - Iterated Elimination of Dominated Strategies (IEDS)
... is only one strategy for each player remaining, that strategy set is the unique Nash equilibrium ... strategy for each player, this strategy set is also a Nash equilibrium ... of weakly dominated strategies may eliminate some Nash equilibria ...
Epsilon-equilibrium - Example
... There are simple examples of stochastic games with no Nash equilibrium but with an ε-equilibrium for any ε strictly bigger than 0 ... and independently from previous stages) is an ε-equilibrium for the game ... Therefore, the game has no Nash equilibrium ...

### Famous quotes containing the words equilibrium and/or nash:

There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages and the ages explained by the hours.
Ralph Waldo Emerson (1803–1882)

If you are really Master of your Fate,
It shouldn’t make any difference to you whether Cleopatra or the Bearded Lady is your mate.
—Ogden Nash (1902–1971)