[1] In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant.
The highest bidder pays the price that was submitted.
[2]: p2 [3] In a FPSBA, each bidder is characterized by their monetary valuation of the item for sale.
Then, if Alice is rational: Alice would like to bid the smallest amount that can make her win the item, as long as this amount is less than
The interesting challenge in such a game is to find a Bayesian Nash equilibrium.
The situation is simpler when the valuations of the bidders are independent and identically distributed random variables, so that the valuations are all drawn from a known prior distribution.
[4]: 234–236 Suppose there are two bidders, Alice and Bob, whose valuations
are drawn from a continuous uniform distribution over the interval [0,1].
We find the best response of Alice to Bob's strategy.
The derivative is (see Inverse functions and differentiation): and it is zero when Alice's bid
satisfies: Now, since we are looking for a symmetric equilibrium, we also want Alice's bid
Denote by: Then, a FPSBA has a unique symmetric BNE in which the bid of player
is given by:[5]: 33–40 The FPSBA is not incentive-compatible even in the weak sense of Bayesian-Nash-Incentive-Compatibility (BNIC), since there is no Bayesian-Nash equilibrium in which bidders report their true value.
However, it is easy to create a variant of FPSBA which is BNIC, if the priors on the valuations are common knowledge.
For example, for the case of Alice and Bob described above, the rules of the BNIC variant are: In effect, this variant simulates the Bayesian-Nash equilibrium strategies of the players, so in the Bayesian-Nash equilibrium, both bidders bid their true value.
The following table compares FPSBA to sealed-bid second-price auction (SPSBA): The auctioneer's revenue is calculated in the example case, in which the valuations of the agents are drawn independently and uniformly at random from [0,1].
agents: In both cases, the auctioneer's expected revenue is 1/3.
The item for sale may not be sold if the final bid is not high enough to satisfy the seller, that is, the seller reserves the right to accept or reject the highest bid.
[8] In contrast, if the seller does not announce the reserve price before the sale but only after the sale, it is a secret reserve price auction.
[9] A FPSBA is distinct from the English auction in that bidders can only submit one bid each.
[3] FPSBA has been argued to be strategically equivalent to the Dutch auction.
[2]: p13 What are effectively FPSBA are commonly called tendering for procurement by companies and organizations, particularly for government contracts and auctions for mining leases.
[3] FPSBA are thought to lead to low procurement costs through competition and low corruption through increased transparency, even though they may entail a higher ex-post extra cost of the completed project and extra time to complete it.