Changes

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.

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==

==Application==

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.

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.

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]]).

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]]).