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]]. | |
| + | 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. | |
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| − | < | + | ==An example== |
| − | + | <div style="float:right"> | |
| − | + | {|style="border-collapse:collapse; background:none; text-align:center" | |
| − | + | | | |
| − | + | | | |
| − | + | !colspan=2 style="padding:0px 0px 6px 0px"|''B'' | |
| − | + | |- | |
| − | + | | | |
| − | + | | | |
| − | + | |style="border-style:solid; border-width:1px; padding:6px"|1 | |
| − | + | |style="border-style:solid; border-width:1px; padding:6px"|2 | |
| − | + | |- | |
| + | !rowspan=2 style="padding:6px 6px 6px 30px"|''A'' | ||
| + | |style="border-style:solid; border-width:1px; padding:6px"|1 | ||
| + | |style="border-style:solid; border-width:1px; padding:6px"|A: bad / B: bad | ||
| + | |style="border-style:solid; border-width:1px; padding:6px"|A: bad / B: good | ||
| + | |- | ||
| + | |style="border-style:solid; border-width:1px; padding:6px"|2 | ||
| + | |style="border-style:solid; border-width:1px; padding:6px"|A: good / B: bad | ||
| + | |style="border-style:solid; border-width:1px; padding:6px; background:#999999"|A: good / B: good | ||
| + | |} | ||
| + | </div> | ||
| + | In the case shown at the right side, participants A and B can choose between "1" and "2". The result can either be "good" or "bad". | ||
| − | + | The highlighted field ("2/2") is the Pareto optimal situation. All other situations can be improved. | |
| − | |||
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| − | + | For example, in "1/2" ("bad" for A, "good" for B), A could switch to "2". The result improves A's result to "good" while leaving B's result unchanged. | |
| − | + | {{clear}} | |
| − | + | ==External links== | |
| − | + | *[http://wilcoxen.cp.maxwell.syr.edu/pages/225.html Pareto Efficiency] by Peter J. Wilcoxen | |
| + | *[http://www.chass.utoronto.ca/~osborne/2x3/tutorial/PE.HTM Definition of Pareto efficiency] by Martin J. Osborne | ||
| − | + | [[category:economics]] | |
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Revision as of 21:31, November 26, 2008
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.
An example
| B | |||
|---|---|---|---|
| 1 | 2 | ||
| A | 1 | A: bad / B: bad | A: bad / B: good |
| 2 | A: good / B: bad | A: good / B: good | |
In the case shown at the right side, participants A and B can choose between "1" and "2". The result can either be "good" or "bad".
The highlighted field ("2/2") is the Pareto optimal situation. All other situations can be improved.
For example, in "1/2" ("bad" for A, "good" for B), A could switch to "2". The result improves A's result to "good" while leaving B's result unchanged.
External links
- Pareto Efficiency by Peter J. Wilcoxen
- Definition of Pareto efficiency by Martin J. Osborne