Meni_Rosenfeld 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.
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.