Tasky comments on Game Theory As A Dark Art - Less Wrong
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Is it rational (even straw-man rational) to enter the dollar auction after one person has already entered it? It should be obvious that you'll both happily keep bidding at least up to $20, that you have at best a 50% chance of getting the $20, and that even if you do get it you will almost certainly make a negligible amount of money even if the bidding stays under $20. So after one person has already bid, it seems like the action "enter this auction" has a clearly negative expected utility.
if another bidder has bid $1, you can enter the auction with 2$ and promise the other bidder $2 if you win the auction.
And then the other bidder bids $3, and promises to give you $1 if he wins the auction. It seems you still haven't avoided the problem of privileging one player's choices.
What if you bid $1, explain the risk of a bidding war resulting in a probable outcome of zero or net negative dollars, then offer to split your winnings with whoever else doesn't bid?