I agree. That includes flipping a coin themselves (because it cannot improve their outcome), nor everyone in the line flipping a coin (because that is not a decision that they can make).
The only decision that cannot be bettered is to flip the coin, thus they ALL flip the coin.
I agreed that such introduces the noise of which you spoke. In reality, all that is needed is the introduction of something outside of the incumbent system. Sometimes noise would help sometimes not.
So, even if they’ve never seen a coin before, they still decide that flipping a coin is the best course of action?
“Flip a coin” is merely a term for “make a random choice”.
Hmmm… Are you taking ‘do nothing’ as the default strategy, i.e. any other strategy is a change from the strategy of ‘do nothing’?
I think if you don’t take ‘do nothing’ to be the default strategy, then ‘pick randomly’ is just as valid. But if ‘do nothing’ is the default strategy, and there’s no expected gain in changing to ‘pick randomly’, there’s an equilibrium in everyone sticking with the default.