Every year I attend a charity auction.  It is of the familiar kind, commonly called an English auction.  The bidders offer a succession of bids, each higher than its predecessors, until no further bid is offered.  The sale is then made to the last bidder, who pays the full amount of his bid.  The auctioneer, a kind of master of ceremonies, facilitates the activity.  He announces each item as the bidding on it is about to begin and suggests an opening bid.  Later, when the bidding lags, he warns the bidders that, unless another bid is offered very soon, he will declare the bidding ended on the current item, which he ultimately does.
        One problem with this arrangement is illustrated by what happens when the number of active bidders has been reduced to two.  Each bidder wants to obtain the item at a price he considers fair to himself but wants to pay no more than he has to.  The result is that the bidding can continue for quite a while, with the bidders alternately offering only a little more than the preceding bid.  Here the auctioneer plays a role.  He calls out an expected minimum value for the next bid, saying, for example, “I have 45, looking for 50,” meaning that the last bid was $45 and that the next one should be at least $50.  This prevents what I call creeping, with the successive bids incrementing in very small steps (perhaps only by pennies).
        The tendency to creep is a natural consequence of the expected behavior of rational bidders.  Each rational bidder has in mind a maximum bid that he is willing to pay for a given item; he will never pay more than this maximum, which in his opinion is the value of the item.  However, he hopes to pay no more than necessary.  What is necessary is the highest among the values assigned by the other bidders, plus a very small amount.
        I think that most observers would agree that typical bidders are to a considerable extent irrational.  In particular they often will not stop when their value for the item has been reached.  It is as if being the winning bidder becomes more important than getting an item at no more than its perceived value.  The auction has come to be viewed as a kind of competition in which the driving idea is, “You cannot outbid me!”  All this is of course of benefit to the sellers, who receive more for the auctioned items than they would if the bidders were rational.  The auction facility, which typically takes a cut from the sellers, also benefits.  Even the bidders appear to be happy, because they keep showing up.  They must find the feeling of competition enjoyable.  The English auction is destined to remain around for a long time.
        However, if the only purpose were to accommodate rational bidders, more efficient alternatives are possible.  A Vickrey auction proceeds as follows:  Each bidder makes a single bid, intended to be the value he assigns to the item.  The bid is sealed, that is, not immediately revealed to the other bidders.  When all the bids have been placed, they are made known, and the highest bidder is identified.  However, he does not pay the amount that he bid; instead he pays the amount of the highest bid made by the other bidders.  The net result is essentially the same as would obtain in an English auction of rational bidders.
        Could a bidder in a Vickrey auction benefit by bidding other than his value for the item?  No.  Bid higher, and he may get stuck for more than he intended.  Bid lower, and he may watch somebody else obtain the item at a price that he would have accepted.
Jethro’s  Jottings
November 7, 2011
with Jethro Flench © 2007-2011.  The views on this web site are opinions.  We reserve the right to exercise our First Amendment rights while we still have them.