This stands in contrast to a private value auction where each bidder's private valuation of the item is different and independent of peers' valuations.
However, each bidder has a different guess about how many quarters are in the jar.
Other, real-life examples include Treasury bill auctions, initial public offerings, spectrum auctions, very prized paintings, art pieces, antiques etc.
One important phenomenon occurring in common value auctions is the winner's curse.
If, on average, bidders are estimating correctly, the highest bid will tend to have been placed by someone who overestimated the good's value.
Rational bidders will anticipate the adverse selection, so that even though their information will still turn out to have been overly optimistic when they win, they do not pay too much on average.
Sometimes the term winner's curse is used differently, to refer to cases in which naive bidders ignore the adverse selection and bid sufficiently more than a fully rational bidder would that they actually pay more than the good is worth.
In the following examples, a common-value auction is modeled as a Bayesian game.
We try to find a Bayesian Nash equilibrium (BNE), which is a function from the information held by a player, to the bid of that player.
We focus on a symmetric BNE (SBNE), in which all bidders use the same function.
[3]: 44–46 There are two bidders participating in a first-price sealed-bid auction for an object that has either high quality (value V) or low quality (value 0) to both of them.
Each bidder receives a signal that can be either high or low, with probability 1/2.
The signal is related to the true value as follows: This game has no SBNE in pure-strategies.
This result is in contrast to the private-value case, where there is always a SBNE (see first-price sealed-bid auction).
[3]: 47–50 There are two bidders participating in a second-price sealed-bid auction for an object.
; the signals are independent and have continuous uniform distribution on [0,1].
Here, there is a unique SBNE in which each player bids: This result is in contrast to the private-value case, where in SBNE each player truthfully bids her value (see second-price sealed-bid auction).
This example is suggested[4]: 188–190 as an explanation to jump bidding in English auctions.
Two bidders, Xenia and Yakov, participate in an auction for a single item.
The valuations depend on A B and C -- three independent random variables drawn from a continuous uniform distribution on the interval [0,36]: Below we consider several auction formats and find a SBNE in each of them.
We find the best response of Xenia to Yakov's strategy.
There are two cases: All in all, Xenia's expected gain (given her signal X) is: where
By the Fundamental theorem of calculus, the derivative of this expression as a function of Z is just
In the above example, in a first-price sealed-bid auction, there is a SBNE with
We find the best response of Xenia to Yakov's strategy.
There are two cases: All in all, Xenia's expected gain (given her signal X and her bid Z) is: where
, the conditional probability-density of Y is: Substituting this into the above formula gives that the gain of Xenia is: This has a maximum when
Common-value auctions are comparable to Bertrand competition.
Firms "bid" prices up to but not exceeding the true value of the item.
The number of firms will influence the success or otherwise of the auction process in driving price towards true value.