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evand comments on Game Theory As A Dark Art - Less Wrong
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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?