Talk:Nash equilibrium

Your changes are excellent but it's not clear to me why you say the Nash equilibrium is sub-optimal for the prisoner's dilemma. Could you elaborate on that a bit more? Thanks.--Aschlafly 19:38, 5 May 2007 (EDT)

Well, the prisoner's dilemma is one of those cases where the Nash equilibrium is not the Pareto optimal solution.

The optimal case would be for both participants to stay silent (in the specific example in the article, both would get six months). However, this is not a Nash equilibrium: If A knows that B chose to stay silent, A would switch to "confess" and improve his own outcome (causing a 10 year punishment for B).

The only Nash equilibrium is the "confess/confess" scenario (in which both prisoners get a 2 year punishment), which is sub-optimal, compared to the possible outcome if both participants cooperated.

I could insert this into the article here, but it would be slightly redundant since this is explained in the PD article (with a fancy table and all that). --JLindon 20:54, 5 May 2007 (EDT)

That's good stuff, and I see your concern about redundancy. I'll supplement the entry and you can improve as you think best. Thanks.--Aschlafly 21:06, 5 May 2007 (EDT)

Very interesting analysis you added there! I think I'll leave it like that for now since I couldn't think of a way to improve it right now. :)

I'm also working on Pareto efficiency (and then redirect Pareto optimum to it) now to remove the red link in the PD article. So far, it's only covered briefly in Efficiency. --JLindon 21:14, 5 May 2007 (EDT)