Assignment 4 -- Four Problems: Direct Derivation of Some Equilibria
You may discuss this assignment with classmates, but all your code and
written work must be your own. Reference all sources.
Please hand in hard copy.
The following problems all deal with single-seller auctions with
private values independently and identically distributed as cdf F(v)
on support [0,1].
I'm asking you to find the equilibrium bidding function directly,
as we have been doing, and I suggest
you do this in value space "bidding as if your value is z".
Shortcuts using revenue equivalence, while they may be elegant and correct,
are jumping ahead and won't get full credit. I want to make sure you understand
how to do these derivations directly.
1. In this problem we consider a Losers Weep auction
with n = 2 bidders and uniform F. In this kind of auction
the high bid wins, losers pay their bids, and the winner gets the item but pays nothing.
2. Do Problem 1. for general number of bidders n and general value
distribution F.
3. In this problem we consider a War of Attrition auction with n = 2
bidders and uniform F. In this kind of auction
the high bid wins, losers pay their bids,
and the winner gets the item and pays the second-highest bid.
Thus, it's a second-price all-pay auction.
4. Do Problem 3. for general number of bidders n and general value
distribution F.
5. (Extra Credit)
Repeat for the Average of Others auction we ran
in class for general number of bidders n and general value distribution F.
Recall that the high bidder wins and pays the average of all the losing bids (but
not her own). Losers pay nothing.