Changes

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 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.

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 no participant is worse off than he was as a result of 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 every participant is strictly better off than he was as a result of the current decision set.  While a strong Pareto optimal set is necessarily weak Pareto optimal, the converse is not necessarily true.

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.

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.