Cooperate or Not? The Nash Equilibrium and the Shapley Value



Nash Equilibrium

"The Nash equilibrium is a stable state of a system that involves several interacting participants in which no participlant can gain by a change of strategy as long as all the other participants remain unchanged."


Make 4 dollars or 5 dollars?
I'll explain it without the traditional prisoner story.

Imagine someone approaches you, as well as a random stranger, on the street. He says to the two of you:

If you both give me a dollar, I will give each of you $5. But if only one of you gives me a dollar, I will keep that dollar, and give $5 only to the person who gives me nothing. You aren't allowed to talk to each other.

Of course, if you could talk to the other player, you would surely agree that you both will give the guy a dollar, and each walk away $4 richer than you were. But since you can't, all you can do is figure out what is best for yourself. And regardless of what the other player chooses, it is best for you to give nothing.

If the other person gives a dollar, you are better off giving nothing -- as you'd make $5 profit rather than only $4. And if he gives nothing, you'll lose nothing, rather than losing a dollar.

The problem, of course, is that both players are likely to think this way, and each give nothing. This results in a lost opportunity to make some free money.

This kind of situation is everywhere in the real world. Rational people make choices that seem (to the Prisoner's-Dilemma naive) to be non-rational. They are not being stupid, they make these choices because it is in their interest to do so.....purely due to inability to make and enforce agreements.

Creativity

John Cleese on creativity:


A 5 Step process for creativity:
In learning any art the important things to learn are, first, Principles, and second, Method. This is true of the art of producing ideas.
Particular bits of knowledge are nothing, because they are made up [of] so called rapidly aging facts. Principles and method are everything.

So with the art of producing ideas. What is most valuable to know is not where to look for a particular idea, but how to train the mind in the method by which all ideas are produced and how to grasp the principles which are at the source of all ideas.

The second important principle involved is that the capacity to bring old elements into new combinations depends largely on the ability to see relationships.

Consequently the habit of mind which leads to a search for relationships between facts becomes of the highest importance in the production of ideas.
STEP 1: GATHERING RAW MATERIAL