A typical application is a seller who wants to sell some items to potential buyers.
The optimal prices depend on the amount that each buyer is willing to pay for each item.
The seller's goal is to design an auction that will produce a reasonable profit even in worst-case scenarios.
PFMs should be contrasted with two other mechanism types: From the point-of-view of the designer, BOM is the easiest, then PIM, then PFM.
The approximation guarantees of BOM and PIM are in expectation, while those of PFM are in worst-case.
A naive approach is to use statistics: ask the potential buyers what their valuations are and use their replies to calculate an empirical distribution function.
Then, apply the methods of Bayesian-optimal mechanism design to the empirical distribution function.
In truthful mechanisms, the agents cannot affect the prices they pay, so they have no incentive to report untruthfully.
be the empirical distribution function calculated based on the valuations of all agents except
If some of these conditions are not true, then the empirical-Myerson mechanism might have poor performance.
Moreover, this example can be generalized to prove that:[1]: 341 In a typical random-sampling mechanism, the potential buyers are divided randomly to two sub-markets.
A consensus-estimate is a function that, with high probability, cannot be influenced by a single agent.
The consensus-estimate function should be selected carefully in order to guarantee a good profit approximation; see Consensus estimate for references.