Nash equilibrium

From Conservapedia

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 (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).