7. A seller announces that he will sell a case of rare wine using a sealed-bid, second-price auction. A group of I indiv
Posted: Sun May 08, 2022 7:59 pm
7. A seller announces that he will sell a case of rare wine
using a sealed-bid, second-price auction. A group of I individuals
plan to bid on this case of wine. Each bidder is interested in the
wine for his or her personal consumption; the bidders’ consumption
values for the wine may differ, but they don’t plan to resell the
wine. So we will view their values for the wine as independent,
private values (as in Chapter 9). You are one of these bidders; in
particular, you are bidder number i and your value for the wine is
vi. How should you bid in each of the following situations? In each
case, provide an explanation for your answer; a formal proof is not
necessary.
(a) You know that a group of the bidders will collude on bids.
This group will chose one bidder to submit a “real bid” of v and
the others will all submit bids of 0. You are not a member of this
collusive group and you cannot collude with any other bidder.
(b) You, and all of the other bidders, have just learned that
this seller will collect bids, but won’t actually sell the wine
according to the rules of a second-price auction. Instead, after
collecting the bids the seller will tell all of the bidders that
some other fictional bidder actually submitted the highest bid and
so won the auction. This bidder, of course, doesn’t exist so the
seller will still have the wine after the auction is over. The
seller plans to privately contact the highest actual bidder and
tell him or her that the fictional high bidder defaulted (he didn’t
buy the wine after all) and that this bidder can buy the wine for
the price he or she bid in the auction. You cannot collude with any
bidder. [You do not need to derive an optimal bidding strategy. It
is enough to explain whether your bid would differ from your value
and if so in what direction.]
using a sealed-bid, second-price auction. A group of I individuals
plan to bid on this case of wine. Each bidder is interested in the
wine for his or her personal consumption; the bidders’ consumption
values for the wine may differ, but they don’t plan to resell the
wine. So we will view their values for the wine as independent,
private values (as in Chapter 9). You are one of these bidders; in
particular, you are bidder number i and your value for the wine is
vi. How should you bid in each of the following situations? In each
case, provide an explanation for your answer; a formal proof is not
necessary.
(a) You know that a group of the bidders will collude on bids.
This group will chose one bidder to submit a “real bid” of v and
the others will all submit bids of 0. You are not a member of this
collusive group and you cannot collude with any other bidder.
(b) You, and all of the other bidders, have just learned that
this seller will collect bids, but won’t actually sell the wine
according to the rules of a second-price auction. Instead, after
collecting the bids the seller will tell all of the bidders that
some other fictional bidder actually submitted the highest bid and
so won the auction. This bidder, of course, doesn’t exist so the
seller will still have the wine after the auction is over. The
seller plans to privately contact the highest actual bidder and
tell him or her that the fictional high bidder defaulted (he didn’t
buy the wine after all) and that this bidder can buy the wine for
the price he or she bid in the auction. You cannot collude with any
bidder. [You do not need to derive an optimal bidding strategy. It
is enough to explain whether your bid would differ from your value
and if so in what direction.]