1. Find a symmetrical Bayesian Nash equilibrium for the auction we ran in class on February 19, 2009: the highest bid wins, and pays the average of all the other bids. Call this type of auction the Average-of-Other-Bids (AVO) auction. Assume that private values are identically, independently, and uniformly distributed on [0,1].
2. Find the best response to truthful bidding for the same auction.
(Extra credit: try extending 1. and 2. to the case where the values are distributed according to a general cdf F.
3. I use the material for this question with permission of Frank S. Robinson (2002), who conducts mail-bid sales of ancient coins. He describes his current sale at http://www.fsrcoin.com/a.html, which closes Tuesday, March 11, 2007 at 11pm. Please see this site for a description of the rules of his auction.
I'm particularly interested in two statements he makes at this site:
PLEASE BID EARLY! In my sales your best strategy is to enter early your top bid, to scare off competition. By waiting till the end you decrease your chances for success & increase the price you have to pay. Also, early bidding is a great help to me in managing the logistics of the sale, so I am highly grateful for early bids.
and
On sale day I will provide by e-mail a list of lots going cheaply.
Here are some further remarks from Frank in email to me (2002). In these remarks Frank refers to the information he reveals when you telephone or email with a bid. In my experience, if you don't become high bidder on a particular item, he will get back with a suggested bid that will make you high bidder on that item. The "going cheaply" list also has a suggested bid level that will make you high bidder on each listed item.
I think the economically rational strategy is exactly what I say -- to put in one's top bid early. If one loses the lot, one is not the poorer, because otherwise would have had to pay more than its worth to the bidder.Your job in this problem is to pretend you're a consultant to Frank. Think about his current choices in running his auction, his problem, his arguments, and compose a response.
Ideally, I'd prefer to run the auction without revealing bid levels. But in practice, it would be disastrous, there are too many people who will not participate on that basis, they don't KNOW how much they should bid. If I tell them, they will bid.
What i should REALLY do is to tell bidders what the SECOND highest bid is, but not reveal the top bid. I keep mulling this over, but always conclude it would not work well in practice.
...
My system actually works VERY well. The real problem for me is getting enough bids early enough to put out a "going cheap" list that doesn't include half the sale! The "going cheap" list is a critical part of the picture!
There are numerous types of incentives I could offer that would cost me money. I'm looking for some brilliant scheme that will be cost-free!