Difference between revisions of "Pareto efficiency"
| Line 31: | Line 31: | ||
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 " | + | 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" is Paretto optimal. |
Generally in a game with finite steps, the efficient outcome may not necessarily be the outcome that maximizes aggregate utility and there may even exist an outcome that has greater utility for every participant. However, in a game with infinite steps, it can be shown that the efficient outcome does maximize aggregate utility. | Generally in a game with finite steps, the efficient outcome may not necessarily be the outcome that maximizes aggregate utility and there may even exist an outcome that has greater utility for every participant. However, in a game with infinite steps, it can be shown that the efficient outcome does maximize aggregate utility. | ||
Revision as of 22:54, 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.
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, other participants' prior and concurrent actions remaining the same, in which at least one participant can improve his own outcome.
If a participant can improve his outcome without harming anybody else, the new decision set Pareto dominates the old one.
An example - 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" is Paretto optimal.
Generally in a game with finite steps, the efficient outcome may not necessarily be the outcome that maximizes aggregate utility and there may even exist an outcome that has greater utility for every participant. However, in a game with infinite steps, it can be shown that the efficient outcome does maximize aggregate utility.
External links
- Pareto Efficiency by Peter J. Wilcoxen
- Definition of Pareto efficiency by Martin J. Osborne