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→An example: I'm basing this last statement off of what I've learned in Game Theory. It's mathematically provable, but I'll provide the needed citations and explanations.
If a participant can improve his outcome without harming anybody else, the new decision set '''Pareto dominates''' the old one.
If a participant can improve his outcome without harming anybody else, the new decision set '''Pareto dominates''' the old one.
==An example==
==An example - Prisoner's dilemna==
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In the case shown at the right side, participants A and B can choose between "1" and "2". The result can either be "very good", "good", "OK", or "bad".
In the one-stage game shown at the right side, participants A and B can concurrently choose between "1" and "2". The result can either be "very good", "good", "OK", or "bad".
The highlighted field ("2/2") is the Pareto optimal situation. All other situations can be improved.
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.
For example, in "1/2" ("bad" for A, "very good" for B), A could switch to "2". The result improves A's result to "OK" while changing B's result also to "OK". However now at "2/2", if B changes to 1, his result becomes "bad". Thus, "2/2" 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.
{{clear}}
{{clear}}