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→When Paretto efficiency is not the equilibrium state - Prisoner's dilemna
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. However, the red field in 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 to "OK" also. 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.
Generally in a game with finite steps, the equilibrium outcome may not necessarily be the Paretto efficient outcome.
Generally in a game with finite steps, the equilibrium outcome may not necessarily be the Paretto efficient outcome.