It is a simple kind of a Bayesian-optimal mechanism, in which the price is determined in advance without collecting actual buyers' bids.
The seller would like to set the price exactly at the buyer's valuation.
In the Bayesian model, it is assumed that the buyer's valuation is a random variable drawn from a known probability distribution.
Suppose the cumulative distribution function of the buyer is
, the expected value of the seller's revenue is:[1] because the probability that the buyer will want to buy the item is
This optimal price has an alternative interpretation: it is the solution to the equation: where
So in this case, BO pricing is equivalent to the Bayesian-optimal mechanism, which is an auction with reserve-price
In this setting, the seller has a single item to sell (with zero cost), and there are multiple potential buyers whose valuations are a random vector drawn from some known probability distribution.
The competition between the buyers may enable the auctioneer to raise the price.
Hence, in theory, the seller can obtain a higher revenue in an auction.
In practice, however, an auction is more complicated for the buyers since it requires them to declare their valuation in advance.
The complexity of the auction process might deter buyers and ultimately lead to loss of revenue.
Blumrosen and Holenstein[2] study the special case in which the buyers' valuations are random variables drawn independently from the same probability distribution.
They show that, when the distribution of the buyers' valuations has bounded support, BO-pricing and BO-auction converge to the same revenue.
: Chawla and Hartline and Malec and Sivan[3] study the setting in which the buyers' valuations are random variables drawn independently from different probability distributions.
Moreover, there are constraints on the set of agents that can be served together (for example: there is a limited number of units).
The approximation factors obtainable by an OPM depend on the structure of the constraints:[3]: 318 Moreover, they show two lower bounds: The approximation factors obtainable by an SPM are naturally better: The lower bound (proved by [2]) is approximately 1.25.
Yan[6] explains the success of the sequential-pricing approach based on the concept of correlation gap, in the following way.
The revenue of a mechanism is related to a set function
Both "Winners" and "Demand" are random-sets, determined by the agents' valuations.
Moreover, by carefully setting the price, it is possible to ensure that each agent
This gives the following approximation factors: In this setting, the seller has several different items for sale (e.g. cars of different models).
The buyer's valuation-vector is a random-vector from a multi-dimensional probability distribution.
The seller wants to compute the price-vector (a price per item) that gives him the highest expected revenue.
Chawla and Hartline and Kleinberg[7] study the case in which the buyer's valuations to the different items are independent random variables.
They show that: They also consider the computational task of calculating the optimal price.
Chawla and Hartline and Malec and Sivan[3] study two kinds of discriminatory pricing schemes: A sequential-pricing mechanism is, in general, not a truthful mechanism, since an agent may decide to decline a good offer in hopes of getting a better offer later.
Then, it is always best for the buyer to accept the first offer (if its net utility is positive).
In the single-parameter setting, there is more competition (since the agents that come from the same buyer compete with each other).
Recently, the SPM scheme has been extended to a double auction setting, where there are both buyers and sellers.