IMSLP Forums

I have been reading through the forums for a while. I never registered because I don't have the time or resources to help IMSLP, and never wanted to be an inactive member of a forum, although I deeply support those who are taking an active part in the project.

I was reading Feldmahler's "Thoughts after the closure of IMSLP" when I came across the profound statement "Weep for our slow but steady descent into the darkness that is Nash equilibrium". This immediately caught my attention. Usually a Nash equilibrium is something to rejoice in, rarely something to weep for.

Let's back up.

A Nash equilibrium is where both parties are doing what is best for themselves, and the other party. This was illustrated in A Beautiful Mind with a bar scene. Nash was working on his thesis, and three of his friends sat at his table when five s walked in, one , the others . One of the friends said "recall the lessons of Adam Smith, the father of modern economics...the best result comes from [both parties] doing what is best for himself." Nash thought about this as his friends conversed about the s, then said "Adam Smith needs revision. If we all go for the , we block each other, and not a single one of us is going to get her. Then we go for her friends, but they will all give us the cold shoulder, because nobody likes to be second choice. The [only choice that will work] is if we all go for her friends. The best result comes from each [party] doing what is best for himself, and the group."

This scenario is very analogous to the scenario concerning IMSLP and UE. UE went for the , blocking IMSLP (although, really both were seeking alternative aspects (romantic and classical) of the same thing). Both parties were in Nash equilibrium before UE wrote the first cease and desist letter, because that was best for both parties individually and collectively. UE went backwards, out of equilibrium, when they shut IMSLP down. Now, equilibrium is approaching again.

Hopefully this sheds some more light on the situation.

I believe you have a slightly wrong interpretation of Nash equilibrium. Read the article on Wikipedia, and especially pay attention to the Prisoner's Dilemma. The examples you have of Nash equilibrium are awfully cute, considering most real world applications of Nash equilibrium. Note that Nash equilibrium does NOT (in fact, in a majority of real life cases) equal the best for the group, nor even the individual (as demonstrated in the Prisoner's Dilemma). It is just what it sounds like: stable. And that is all it really is (unfortunately).

"Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill's decision, and Bill is making the best decision he can, taking into account Amy's decision."

Aha - this is what I misinterpreted.


What if we were to unite these?

A makes the best decision considering B's best decision

B makes the best decision considering A's best decision

and

A does what is best for A and B

B does what is best for A and B


Each dilemma has not two, but three solutions.


Let's consider the prisoner's dilemma.


Quote from Wikipedia:

"Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act?"

The third solution is for A and B to escape, or bribe the questioners.

The third solution, likewise, for IMSLP and UE is for UE to be a member of IMSLP and have admin rights, and freely delete scores that are legitimately out of 50 yr post mortem copyright. Maybe there is a better solution.

Since we have arrived at a non-conclusive conclusion, I think we can safely assume that I was wrong, that the two theorems cannot be united.

The third choice you gave in the prisoner's dilemma breaks the game itself, and so is invalid (they can also fly away on the private jet of a friend of theirs who infiltrated the prison camp and managed to conceal the jet among the trees, and infinite other possibilities). This is a game, and not real life. The beauty (or ugliness) is that most real life decisions can be reduced to somewhere along the Nash equilibrium scale, depending on the amount of trust. Even escaping prison can be evaluated along the scale.

A and B are in Nash equilibrium if A is making the choice given that B will attempt to secure the most overall beneficial choice solely for B him/herself, with no trust in A (which is in many cases the worst choice B can make from A's point of view). And vice versa. Nash equilibrium is reached when all trusts vanishes. The first paragraph in the Wikipedia article summarizes the equilibrium nicely.

Therefore, the example in your first post about dating is the exact opposite of Nash equilibrium, which I like to call Nash anti-equilibrium. Yes that solution is the best for the group, but it is also the most unstable. Anyone in that group can have gains by changing their strategy (going for the main girl). Either there is a context issue on that quotation, or someone didn't do enough research while writing the script .

Nash equilibrium is not a good thing. In its purest form it completely disintegrates any social bond and trust. And the result is in the worst interests of the group itself. In quite a direct sense, Nash equilibrium is almost exactly like cancer.

In any case, I agree that in most cases Nash equilibrium cannot be united with the most optimal action of the group as a whole. By the way, my sentence that you quoted was not directed at the UE/IMSLP dispute per se, but a more general comment.