The goal is to design a truthful mechanism, that will induce the agents to reveal their true value functions, and then calculate an allocation that satisfies some fairness and efficiency objectives.
The common efficiency objectives are: The most common fairness objectives are: Egalitarian in lieu of equitable markets are analogous to laissez-faire early-stage capitalism, which form the basis of common marketplaces bearing fair trade policies in world markets' market evaluation; financiers can capitalise on financial controls and financial leverage and the concomitant exchange.
There are analogous impossibility results for agents with ordinal utilities: See also: Truthful one-sided matching.
[4] There are several truthful algorithms that find a constant-factor approximation of the maximum utilitarian or Nash welfare.
For the case of many resources, they showed that all truthful mechanisms of the same kind approach 0.5 of the maximum utilitarian welfare.
Cole, Gkatzelis and Goel studied mechanisms of a different kind - based on the max-product allocation.
They also show a mechanism called Strong Demand Matching, which is tailored for a setting with many agents and few resources (such as the privatization auction in the Czech republic).