Nash equilibrium
From Conservapedia
The Nash equilibrium is the set of decisions by multiple rivals by which they maximize their individual self interests in a like-minded manner. The solution is different from when someone maximizes his self-interest in the hope that similarly situated participants act differently. The Nash equilibrium assumes that all similarly situated participants act in a similar manner.
The "equilibrium" is the set of decisions such that no individual participant, acting alone, can gain anything by altering his decision. If he were able to improve his position, then he would, thereby disqualifying that set of decisions as the "equilibrium". This is similar to a chemical equilibrium or a steady-state solution in physics, whereby each individual maximizes his own gain based on similar actions by similarly situated participants.
The Nash equilibrium is named after John Nash, a mathematician. It is a topic in game theory, and its significance was recognized by award of the Nobel Prize in Economics.
The Nash equilibrium is a modification to the strict self-interest predicted by Adam Smith, because the Nash equilibrium takes into account the influence of competitors' decisions on the primary decision-maker.
Application
The Nash equilibrium 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 (non-Pareto optimal) result that could be improved if both participants cooperated and changed their decisions (by neither confessing to the crime). But left on his own, no single participant would change his decision because he would be individually worse off for doing so.
Observe that in situations where the Nash equilibrium fails to attain the most efficient outcome for the individual participants, it does deliver the most benefits to the customer (in the case of an oligopoly) or to the prosecutor (in the case of the prisoner's dilemma).
