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Slider comments on The Number Choosing Game: Against the existence of perfect theoretical rationality - Less Wrong Discussion
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Define a "sucker" option to be a an option with a lower utility value than a some other possible choice.
A dominant decision is never a sucker option but a perfect agent migth end up choosing a sucker option. In the number naming game every option is a sucker option.
Thus "winning" is different from "not losing".
I would argue that a perfect agent can never choose a "sucker" option (edit:) and still be a perfect agent. It follows straight from my definition. Of course, if you use a different definition, you'll obtain a different result.
Thus why the dominant agent can't play the number naming game as it can't choose any of the options.