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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.

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==

==When Pareto efficiency is not the equilibrium state - Prisoner's dilemna==

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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".

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.

The green field ("not confess/not confess") is the Pareto optimal situation; the red field is the [[Nash equilibrium]] solution.

There exists no other decision set besides "not confess/not confess" that has an equal or better outcome for all participants.  However, in "not confess/not confess" ("good" for A, "good" for B), A could switch to "confess". Assuming B does not change his decision, this improves A's result to "very good" while changing B's result to "bad".  (There is no honor among thieves, so A is not concerned about B's welfare.)  Knowing this, if B also changed his decision to "confess", B's result improves to "OK".  However, A's result would then worsen, but only down to "OK" as well.  Now at "confess/confess", if either A or B unilaterally changes to "not confess", his result worsens to "bad".  Thus, "confess/confess", and not the '''Pareto optimum''', would be the equilibrium outcome.

There exists no other decision set besides "not confess/not confess" that has an equal or better outcome for all participants.  However, in "not confess/not confess" ("good" for A, "good" for B), A could switch to "confess". Assuming B does not change his decision, this improves A's result to "very good" while changing B's result to "bad".  (There is no honor among thieves, so A is not concerned about B's welfare.)  Knowing this, if B also changed his decision to "confess", B's result improves to "OK".  However, A's result would then worsen, but only down to "OK" as well.  Now at "confess/confess", if either A or B unilaterally changes to "not confess", his result worsens to "bad".  Thus, "confess/confess", and not the '''Pareto optimum''', would be the equilibrium outcome.