A seller announces that he will sell a case of rare wine using a sealed-bid, secondprice auction. A group of I individuals plans 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 view their values for the wine as independent, private values (as earlier in this chapter). 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 choose 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 have 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.)
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