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Then the common use of the "assumption of common rationality" is different than the "assumption of infinite rationality" that you used in setting up this problem.
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Nope.
http://en.wikipedia.org/wiki/Common_knowledge_(logic)
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Then the accepted answer is wrong. Come up with a couterargument that isn't an argument from authority.
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someone smarter than i am can probably do this better, but my best guess is there's some sort of circularity i can't quite pin down.
maybe the entire rationality of your strategy depends on it being the rational strategy.
maybe it's a problem that you expect to use the same strategy
because only one solution is rational, and you use that fact to decide
which is the rational one.
maybe you have to say "we will both choose the same solution given that we choose the rational one" and not just "we will both choose the same solution." (100/100) maximizes your payoff if you both choose the same strategy, which we know happens if you both choose the rational strategy, which makes 100 the rational strategy. it seems like there could be a problem somewhere.
even though you say you are sure that 100 is the only rational solution, you
don't claim that you know for sure (beforehand) that your rational opponent will bid 100. it seems like it should follow from "there is only one rational solution" that you also know your opponent will play it ahead of time.
maybe once you start assuming that your opponents bid
depends on your own, you've already left rationality behind, even though the whole thing appears to be rational on the surface.
playing 100 maximizes your payoff as long as it's the rational strategy, and it's the rational strategy because it maximizes your payoff. but of course it doesn't maximize your payoff against an opponent playing "the rational strategy," but we've already proven it's the rational strategy, so it must be the case that sometimes the rational strategy does not maximize its own payoff given the rational strategy of the opponent.
i dont know, [censored] it.