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adsenanim comments on Mixed strategy Nash equilibrium - Less Wrong
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Comments (46)
Nice Job!
Can you relate this to Parrondo's Paradox?
Now that I've looked it up, I don't think it really has the same intuitions behind it as mixed strategy NE. But it does have an interesting connection with swings. If you try to push a heavy pendulum one way, you won't get very far. Trying the other way you'll also be out of luck. But if you push and pull alternately at the right frequency, you will obtain an impressive amplitude and height. Maybe it is because I've had firsthand experience with this that I don't find Parrondo's paradox all that puzzling.
From what you are saying, with the mixed strategy NE, I get that possible moves increase in relation to the complexity of the equilibrium, so that it becomes increasingly likely that any possible action could have an added emphasis that would cause a specific outcome as the equilibrium increases in complexity.
e.g.
What you are describing with the pendulum motion, the pendulum does not require additional effort in both directions to increase, only one direction, and the effort need be only the smallest (or smaller in addition) in relation to the period, and direction. An action to large in the same direction, or against the direction will destabilize it.
Isn't it true that the more precise the equilibrium, the less effort is required to destabilize it?
I think that the main difference between our arguments is that while you are talking of simultaneous action, I am talking of sequential action...
Sorry, I'm not sure I know how to answer that.
The more complex a system becomes, the easier it is to destabilize it.
Is this a conditional argument?