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Matt_Simpson comments on Swords and Armor: A Game Theory Thought Experiment - Less Wrong
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But green sword/blue armor loses to something else. Dominance reasoning isn't supposed to guarantee that your strategy beats everyone.
OTOH, my 4x4 table doesn't look like the one rosyatrandom linked to, so I may have made a computational error.
Oh! I thought you were using the game-theoretic definition of "dominance", where one strategy always beats (or always beats or matches) another strategy. For example, in this game, any red-sword strategy is dominated by the corresponding blue-sword strategy.
Well I was, but I didn't mean to say that blue/green dominates everything else (imprecise language on my part). If you iteratively remove dominated strategies on both sizes you're left with blue/green - which is thus a Nash Equilibrium. At least on my table, but I don't trust my numbers anymore.