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James_K comments on Swords and Armor: A Game Theory Thought Experiment - Less Wrong
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I've given the problem a quick pass and I can conclude this much:
1) Using the red weapon is weakly dominated, so definitely don't do that.
2) There's no Nash equilibrium in pure strategies, so if there's an equilibrium, it's in mixed strategies. If I have time over the weekend, I might re-learn how to do Lagrange Multiplier calculus and then I'll have a go at calculating a mixed strategy equilibrium.