Topics Applications Auctions Bargaining Experimental Economics Forum General Equilibrium Napster other Other Topics Prisoners Dilemma Zero Sum Games
  Thread and Full Text View
Taking logs,
lnU = ln(vb) + (n1)lnb + constant terms.
Differentiating by b, it follows that buyer 1's best response is to bid b(v)
= (n1)v/n. Exactly the same agument holds for each bidder. Thus the
equilibrium bidding strategy is b(v) = (n1)v/n. It is also not difficult
to confirm that the expected high bid (hence expected revenue) is (n1)/(n+1).
Next suppose that bidder n is allowed to match. Let b be the high bid
among the n1 other buyers. Bidder n will match if his valaution
exceeds b. Thus bidder n matches with probability Pr{vn
< b} = b. It follows that bidder 1 wins with a bid
of b with probabilty H(b) = b(kb)^(n2).
Arguing as before,
U(v,b) = (vb)H(b).
Taking logs,
lnU = ln(vb) + (n1)lnb + constant terms.
Differentiating by b, it follows that buyer 1's best response is to bid b(v)
= (n1)v/n. Thus with one biider matching, the bidding strategy is the same
as if all n bidders were bidding. Note also that if bidder 1 drops out completely,
ther are n1 bidders so the new equilibrium is b(v) = (n2)v/(n1).
Thus adding the nth bidder (whether or not he matches or bids like the other raises
the bids of all players.
What about revenue? It is not difficult to coinfirm that with bidder n
matching, revenue is ((n1)/n)^2.
We thus have the following revenue results.
N bidders all bidding symmetrically Revenue = (n1)/(n+1)
N bidders with 1 of them matching Revenue = ((n1)/n)^2
N1 bidders all bidding symmetrically Revenue = (n2)/n
[Manage messages]
01/17/2000 01:23 PM by name withheld; Some more details of the problem  Background
Developer (D) is developing a power plant and wishes to seek competitive
bids for fuel supply. There are five (5) qualified bidders, Companies 1  5,
all who are capable of supplying fuel. D will be required to [View full text and thread]
What happens in auctions depends both on the circumstances of the auction and the rules. One
possibility is that the bidders have private information relevant to the other bidders  for
example some inside information about future [View full text and thread]
01/15/2000 10:41 AM by name withheld; What happens when one bidder has an advantage?  The background is that our company has offered to provide
development funding to X in exchange for the right to
match the best offer to supply them with fuel. Assume the
development funding is adequate value for the option received. [View full text and thread]
