Question

Out of the four types of auctions, which one results in the highest expected revenues for the seller in a common-value auction? Which one results in the lowest expected price paid for the buyer in a common-value auction? Explain.

Answer 1

He established four major (one-sided) auction types: (1) the ascending-bid (open, oral, or English) auction; (2) the descending-bid (Dutch) auction; (3) the first-price, sealed-bid auction; and (4) the second-price, sealed-bid (Vickrey) auction.

we have assumed that bidders’ values for the item being auctioned are independent: each bidder knows her own value for the item, and is not concerned with how much it is worth to anyone else. This makes sense in a lot of situations, but it clearly doesn’t apply to a setting in which the bidders intend to resell the object. In this case, there is a common eventual value for the object — the amount it will generate on resale — but it is not necessarily known. Each bidder i may have some private information about the common value, leading to an estimate vi of this value. Individual bidder estimates will typically be slightly wrong, and they will also typically not be independent of each other. One possible model for such estimates is to suppose that the true value is v, and that each bidder i’s estimate vi is defined by vi = v + xi, where xi is a random number with a mean of 0, representing the error in i’s estimate.

Auctions with common values introduce new sources of complexity. To see this, let’s start by supposing that an item with a common value is sold using a second-price auction. Is it still a dominant strategy for bidder i to bid vi? In fact, it’s not. To get a sense for why this is, we can use the model with random errors v + xi. Suppose there are many bidders, and that each bids her estimate of the true value. Then from the result of the auction, the winning bidder not only receives the object, she also learns something about her estimate of the common value — that it was the highest of all the estimates. So in particular, her estimate is more likely to be an over-estimate of the common value than an under-estimate. Moreover, with many bidders, the second-place bid — which is what she paid — is also likely to be an over-estimate. As a result she will likely lose money on the resale relative to what she paid.

This is known as the winner’s curse, and it is a phenomenon that has a rich history in the study of auctions. Richard Thaler’s review of this history [387] notes that the winner’s curse appears to have been first articulated by researchers in the petroleum industry . In this domain, firms bid on oil-drilling rights for tracts of land that have a common value, equal to the value of the oil contained in the tract. The winner’s curse has also been studied in the context of competitive contract offers to baseball free agents with the unknown common value corresponding to the future performance of the baseball player being courted.

Rational bidders should take the winner’s curse into account in deciding on their bids: a bidder should bid her best estimate of the value of the object conditional on both her private estimate vi and on winning the object at her bid. That is, it must be the case that at an optimal bid, it is better to win the object than not to win it. This means in a common-value auction, bidders will shade their bids own ward even when the second-price format is used; with the first-price format, bids will be reduced even further. Determining the optimal bid is fairly complex, and we will not pursue the details of it here. It is also worth noting that in practice, the winner’s curse can lead to outright losses on the part of the winning bidder , since in a large pool of bidders, anyone who in fact makes an error and overbids is more likely to be the winner of the auction. In these cases as well as others, one could argue that the model of common values is not entirely accurate.

One oil company could in principle be more successful than another at extracting oil from a tract of land; and a baseball free agent may flourish if he joins one team but fail if he joins another. But common values are a reasonable approximation to both settings, as to any case where th