Difference between revisions of "Nash equilibrium"
(Moved a few sections around, rewrote the intro, transformed the note about the PD into a section about counter-intuitive results) |
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| − | + | In [[Game Theory]], the '''Nash equilibrium''' (named after [[John Nash]]) is a state in which no participant would gain anything by only changing his own decision after learning of the other participants' decisions. The implied assumption is that no other participant will change his decision. A problem can have more than one Nash equilibrium. | |
| − | The Nash | + | ==Application== |
| + | The Nash equlibrium is used to describe situations when several people or companies have benefits that depend on the decisions of rival. The Nash equilibrium predicts the choices those people or companies will make to maximize their individual benefits. | ||
In economics, the Nash equilibrium describes pricing decisions by an oligopoly. The set of selling prices will be such that no seller can benefit by changing his price while the other sellers keep their prices unchanged. If the cost structures are the same for each seller in an oligopoly, then the Nash equilibrium is where the price equals the marginal cost, or P=MC. | In economics, the Nash equilibrium describes pricing decisions by an oligopoly. The set of selling prices will be such that no seller can benefit by changing his price while the other sellers keep their prices unchanged. If the cost structures are the same for each seller in an oligopoly, then the Nash equilibrium is where the price equals the marginal cost, or P=MC. | ||
| − | + | ==Nash equilibrium and intuition== | |
| + | There are cases in which the Nash equilibrium is a counter-intuitive outcome (and where the intuitive outcome is not a Nash equilibrium). The reason for this is the assumption that a participant assumes that nobody except for him will potentially change strategies. | ||
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| + | One notable example is the [[Prisoner's dilemma]], in which the Nash equilibrium is a sub-optimal result that could be improved if both participants cooperated and changed their decisions. But left on his own, no single participant would change his decision. | ||
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[[category:mathematics]] | [[category:mathematics]] | ||
[[category:economics]] | [[category:economics]] | ||
Revision as of 21:20, May 5, 2007
In Game Theory, the Nash equilibrium (named after John Nash) is a state in which no participant would gain anything by only changing his own decision after learning of the other participants' decisions. The implied assumption is that no other participant will change his decision. A problem can have more than one Nash equilibrium.
Application
The Nash equlibrium is used to describe situations when several people or companies have benefits that depend on the decisions of rival. The Nash equilibrium predicts the choices those people or companies will make to maximize their individual benefits.
In economics, the Nash equilibrium describes pricing decisions by an oligopoly. The set of selling prices will be such that no seller can benefit by changing his price while the other sellers keep their prices unchanged. If the cost structures are the same for each seller in an oligopoly, then the Nash equilibrium is where the price equals the marginal cost, or P=MC.
Nash equilibrium and intuition
There are cases in which the Nash equilibrium is a counter-intuitive outcome (and where the intuitive outcome is not a Nash equilibrium). The reason for this is the assumption that a participant assumes that nobody except for him will potentially change strategies.
One notable example is the Prisoner's dilemma, in which the Nash equilibrium is a sub-optimal result that could be improved if both participants cooperated and changed their decisions. But left on his own, no single participant would change his decision.