Changes

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.)  However knowing this, if B also changed his decision to "confess", B's result improves to "OK" while A's result worsens to "OK".  Now at "confess/confess", if either A or B unilaterally changes to "not confess", his result worsens to "bad".  Thus, "confess/confess", and 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.)  However knowing this, if B also changed his decision to "confess", B's result improves to "OK", but A's result would then worsen to "OK".  Now at "confess/confess", if either A or B unilaterally changes to "not confess", his result worsens to "bad".  Thus, "confess/confess", and 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.