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casebash comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong
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It isn't so much that fact that you don't obtain the (non-existant) maximum that is important, it's the fact that another agent beats you when nothing was stopping you beating the agent.
Is utility zero-sum in this scenario? If I'm hyper-ultra-happy, and my neighbor is extra-super-über-mega-happy, that does not necessarily mean he beat me.
Okay, let me restate it. It's the fact that a different version of yourself that choose the same number as your neighbour would have done better than what you did. Nothing to do with zero-sum.