Difference between revisions of "Pareto efficiency"
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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 | + | 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 efficiency 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 is strictly better off and 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 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. | 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 is strictly better off and 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 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. | ||
Revision as of 23:54, August 13, 2009
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 efficiency 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 is strictly better off and 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 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 improves without anybody else's outcome worsening, the new decision set Pareto dominates the old set.
When Paretto efficiency is not the equilibrium state - Prisoner's dilemna
| B | |||
|---|---|---|---|
| not confess | confess | ||
| A | not confess | A: good / B: good | A: bad / B: very good |
| confess | A: very good / B: bad | A: OK / B: OK | |
In the one-stage game shown at the right side, prisoners A and B can concurrently choose between "not confess" and "confess". The result can either be "very good", "good", "OK", or "bad".
The green field ("not confess/not confess") is the Pareto optimal situation. However, the red field in the Nash equilibrium solution.
However, the Pareto optimal solution is not the equilibrium solution. For example, in "not confess/confess" ("bad" for A, "very good" for B), A could switch to "confess". The result improves A's result to "OK" while changing B's result also to "OK". However now at "confess/confess", if B changes to "not confess", his result becomes "bad". Thus, "confess/confess" would be the equilibrium outcome.
Generally in a game with finite steps, the equilibrium outcome may not necessarily be the Paretto efficient outcome.
External links
- Pareto Efficiency by Peter J. Wilcoxen
- Definition of Pareto efficiency by Martin J. Osborne