Editing Mechanism design (section)

===Revenue equivalence theorem===
{{main|Revenue equivalence}}

{{harvs|txt|last=Vickrey|year=1961|author-link=William Vickrey}} gives a celebrated result that any member of a large class of auctions assures the seller of the same expected revenue and that the expected revenue is the best the seller can do. This is the case if
# The buyers have identical valuation functions (which may be a function of type)
# The buyers' types are independently distributed
# The buyers types are drawn from a [[Continuous distribution#Continuous probability distribution|continuous distribution]]
# The type distribution bears the monotone hazard rate property
# The mechanism sells the good to the buyer with the highest valuation

The last condition is crucial to the theorem. An implication is that for the seller to achieve higher revenue he must take a chance on giving the item to an agent with a lower valuation. Usually this means he must risk not selling the item at all.