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Coscott comments on Open Thread February 25 - March 3 - Less Wrong
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I do not think this is correct. First, the host should only offer you the chance to switch if you are winning, so the chance should be 0. Second, this example seems too contrived to be something that we would have evolved a good instinct about.
Unless they're trying to trick you. The problem collapses to a yes or no question of whether one of you is able to guess the level the other one of you is thinking on
Um, no, the only Nash equilibria are where you never accept the deal. If you ever accept it at all, then they will only offer it when it hurts you.