There are n agents, each of whom has a personal function that attributes a numeric value to each "bundle" (combination of resources).
Crucially, some resources may have to be discarded, i.e., free disposal is assumed.
In contrast, PA does not use monetary payments, and the agents' utilities are reduced by a multiplicative factor, by taking away some of their resources.
However, there is provably no truthful mechanism that can guarantee to each agent more than 0.5 of the max-product utility.
The PAM has been used as a subroutine in a truthful cardinal mechanism for one-sided matching.