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Spurlock comments on Game Theory As A Dark Art - Less Wrong
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AFAICT, this is an unfortunately strong argument... Thanks.
I see two solutions to the paradox:
1) Note that auctions are usually played by more than 2 bidders. Even if the first bidder would let you have the pot for $2, the odds that you'll be allowed to have it by everyone decrease sharply as the number of participants increases. So in a real auction (say at least 5 participants), 9% probably is overconfident.
2) If we have a small number of bidders, one would have to find statistics about the distribution of winners on these auctions (10% won by first bid, 12% won on second bid, and so on...). Of course, this strategy only works if your opponents don't know (and won't catch on) that you never bid more than once. But it should work at least for a one-shot auction where you don't publish your strategy in advance.
Out of curiosity, since you argue that joining these auctions as player #2 could very well have positive EU, would you endorse the statement "it is rational to join dollar auctions as the second bidder"? If not, why not?
Against typical human opponents it is not rational to join dollar auctions either as the second player or as the first, because of the known typical behavior of humans in this game.
The equilibrium strategy however is a mixed strategy, in which you pick the maximum bid you are willing to make at random from a certain distribution that has different weights for different maximum bids. If you use a the right formula, your opponents won't have any better choice than mirroring you, and you will all have an expected payout of zero.