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]]. | 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]]. | ||
| − | 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 | + | 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: |
| + | #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 | + | If a participant can improve his outcome without hurting anybody else, the new decision set '''Pareto dominates''' the old one. |
| − | == | + | ==When Paretto efficiency is not reached - Prisoner's dilemna== |
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The highlighted field ("confess/confess") is the Pareto optimal situation. All other situations can be improved. | The highlighted field ("confess/confess") is the Pareto optimal situation. All other situations can be improved. | ||
| − | 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" | + | 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 | + | Generally in a game with finite steps, the equilibrium outcome may not necessarily be the Paretto efficient outcome. However, in a game with infinite steps, it can be shown that the equilibrium outcome is the Paretto efficient outcome. |
{{clear}} | {{clear}} | ||
Revision as of 23:05, 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.
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:
- 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.
When Paretto efficiency is not reached - 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 highlighted field ("confess/confess") is the Pareto optimal situation. All other situations can be improved.
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. However, in a game with infinite steps, it can be shown that the equilibrium outcome is the Paretto efficient outcome.
External links
- Pareto Efficiency by Peter J. Wilcoxen
- Definition of Pareto efficiency by Martin J. Osborne
