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whpearson comments on Mixed strategy Nash equilibrium - Less Wrong
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You can read the problem description as requiring you to only pick one set of sword + armour ( which makes sense in terms of cost of equipment etc ). So the answer "mixed strategy" may or may not be allowed. Although it can be used as reasoning for why you picked the colour combination you did.
The problem isn't well specified, are you allowed to know the current population, or history? If mixed strategies are not allowed, then all you should do is look at the current distribution of players before making a decision.
I suppose what I am saying is that while the problem statement mentioned game theory, the actual question indicated a non-game theoretic answer by not allowing mixed strategy.
I think you're making a distinction between one-shot and iterated games. This is a different distinction than that between mixed and non-mixed strategies. You can have a mixed strategy equilibrium in a one-shot game, as in both the swords-n-armour example and the attack/defend East/West example.
So: if the game is one-shot (and you can see the current distribution), the right decision depends only on the current distribution, as you said.
The question was
My point was that you can't say mixed strategy to the first question, although it is a valid answer to the second part.
You could say yellow/yellow, because that was the value selected by my RNG using the mixed strategy distribution Z.
But yes I was being imprecise with my language, I'm a little rusty. I'll fix once I have had some sleep.
But if you can't look at the current distribution, you still need to use the equilibrium for this single choice. Otherwise, you're at risk that everyone will think the same as you, except for a few smarter players who will counter it.