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In both popular level books on economics/rationality/etc., and videos of actual economics lectures, I keep running into the suggestion to bid in a common value auction as though victory is already guaranteed. For example, from this Yale lecture...

So the lesson here is, bid as if you know you win. Now why is that a good idea? Let’s go back to this case of now you discover you’ve won. Provided you bid as if you know you won, when you win you’re not going to be disappointed because you already took that information into account. But if you bid not as if you won, you failed to take into account the possibility of winning, then winning’s going to come as a shock to you and cause regret. So the only way to prevent this ex-post regret, the only way to bid optimally, is to bid as if you know you’re going to win. Estimate the number of coins not on your own sample but on the belief that your sample is the biggest sample.

This makes very little sense in my mind. I understand why the winner's curse emerges from naive bidding, but the prescription for countering it seems silly. If I condition my bid on the knowledge that I'm certainly going to win, then my bid will be the second lowest bid possible (in other words, the lowest bid that could actually be a winning bid). If I am restricting my view of what outcomes may occur to the possible worlds where I win the auction, then my optimal bidding strategy would be to select one of those worlds in which I pay the lowest cost for the item. On the other hand, if I do not allow my strategy to vary in response to the stipulated information that victory is guaranteed, then I will end up bidding as though I do not know of the winner's curse construct.

What is going wrong in my thinking about this prescription?

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  • $\begingroup$ It does not say that you should behave as if you are "certainly going to win". $\endgroup$
    – Michael Greinecker
    Dec 4, 2022 at 21:34
  • $\begingroup$ @MichaelGreinecker The quote says, for example, "bid as if you know you win," "bid as if you know you won," and "bid as if you know you're going to win." I don't see in what way this differs from bidding as if you are certainly going to win. $\endgroup$
    – user10478
    Dec 5, 2022 at 3:06
  • $\begingroup$ The quote tells you that you should bid in a way that is optimal conditional on winning; you should bid so that your bid would be still optimal if you would know it is the winning bid. $\endgroup$
    – Michael Greinecker
    Dec 5, 2022 at 7:32
  • $\begingroup$ @MichaelGreinecker In my mind, the bid that is optimal conditional on winning is the same as the smallest bid that could possibly win. What is the difference? $\endgroup$
    – user10478
    Dec 6, 2022 at 6:02
  • $\begingroup$ If you win with a very low bid, it must be that everyone else made a higher bid and this is the information you should take into account. It does not mean that the event that your bid is the winning bid is guaranteed irrespective of everyone else's behavior. $\endgroup$
    – Michael Greinecker
    Dec 6, 2022 at 9:55

1 Answer 1

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Consider an auction with 100 buyers. Each buyer receives a private signal of the object. Suppose that after receiving your signal, you calculate that the expected value of the object is \$10. One might conclude 'I'll bid \$9 and every time I win the auction I'll make 1 dollar'. On the face, that seems reasonable. So you bid \$9 and it turns out you win! But you start asking the 99 other buyers what they thought the object is worth...it turns out that all 99 of them thought the value of the object was less than 10 dollars (this is almost by definition as you won the object). This means that the object is likely much less than \$10 and you bid more than the object was worth. This is essentially the winner's curse.

I don't really like the passage you quoted, I can see how it is a bit confusing. I would rephrase it as follows

The fact that you win an auction has informational content. That content being that you only win an auction when the 99 other buyers received a signal lower than your own. Therefore, in the event that you win, the object is certainly worth less than your initial belief. If you fail to take this information into account, you are likely to bid more than the object is worth.

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  • $\begingroup$ Hmm, I appreciate the explanation of the winner's curse, but this doesn't really offer a prescription for how to take the information into account as the passage purports to offer (albeit with some confusion or error). I do have an idea for this; maybe you can tell me if it's correct or not. In order for a company or team to account for the winner's curse, have one member receive the signal, calculate the "prior" expected value of $10, and plug it into Bayes' Theorem to calculate a "posterior" expected value conditional on knowing with certainty that they will win the auction. $\endgroup$
    – user10478
    Dec 7, 2022 at 4:42
  • $\begingroup$ Then hand the posterior expected value to a second team member, preferably someone who does not even know about the winner's curse, and have them bid without any information about whether they will win or not. Implemented as an individual, the prescription would be "value the item as though you know you are going to win, then bid as though you no longer know." This would mean the passage is false, at least without some extremely charitable interpretation. Is this the correct way to account for the winner's curse? $\endgroup$
    – user10478
    Dec 7, 2022 at 4:46
  • $\begingroup$ Bah, too late to edit comment. On second thought, I guess you can't actually use Bayes' Theorem on an expected value, but I still feel like this thought is in the direction of a correct answer...maybe. $\endgroup$
    – user10478
    Dec 7, 2022 at 4:53

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