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In [[game theory]] and [[economics]], the concept of '''Pareto efficiency''' (or '''Pareto optimality''') is a method to judge the [[efficiency]] of a set of decisions made by the participants. It was named after [[Vilfredo Pareto]].  Paretto eficiency is different from and should not be confused with [[Nash equilibrium]].

In [[game theory]] and [[economics]], the concept of '''Pareto efficiency''' (or '''Pareto optimality''') is a method to judge the [[efficiency]] of a set of decisions made by the participants. It was named after [[Vilfredo Pareto]].  Paretto eficiency is different from and should not be confused with [[Nash equilibrium]].

A set of decisions "x/y" (meaning that participant A chooses "x" while participant B chooses "y") is called Pareto optimal if there is '''no''' other state in which:

A decision set (a combination of all decisions made by all participants) is called '''strong Pareto optimal'' if there is no other set in the entire decision space (all possible decision sets) in which at least one participant can improve his own outcome while no other participant receives a worse outcome than he does in the current decision set. A decision set is called '''weak Pareto optimal''' if there is no other set in the entire decision space (all possible decision sets) in which at least one participant can improve his own outcome without each participant receiving a strictly better (not equal) outcome than he does in the current decision set.  While a strong Pareto optimal set is necessarily weak Pareto optimal, the converse is not necessarily true.

#at least one participant can improve his own outcome while

#no other participants receives a worse outcome than he does now.

Putting it into less formal style: As long as a player can improve his outcome without hurting anybody else, the situation is not Pareto efficient.

If a participant can improve his outcome without hurting anybody else, the new decision set '''Pareto dominates''' the old one.

If there exist a decision set where at least one participant's outcome is improved without anybody else being hurt, the new decision set '''Pareto dominates''' the old set.

==When Paretto efficiency is not the equilibrium state - Prisoner's dilemna==

==When Paretto efficiency is not the equilibrium state - Prisoner's dilemna==