Myerson's lemma
In a single-dimensional setting a mechanism is truthful exactly when its allocation rule never penalises a higher report, and the payments are then pinned down up to a constant.
In a single-dimensional setting a mechanism is truthful exactly when its allocation rule never penalises a higher report, and the payments are then pinned down up to a constant.
Often misread asHunting for a clever payment rule that will make a non monotone allocation truthful, when no such payment rule exists.
How to see it
Fix who wins and the payments are forced
Where each participant's private information is a single number, truthfulness turns on one thing only: a higher report must never get you less of the good. Once the allocation rule has that property, the payments that make honesty optimal are determined, with no freedom left beyond a constant.
The checkMonotonicity of the allocation is necessary, not merely convenient. If raising your report can cost you the object, no payment scheme anywhere can repair it.
Try itPropose awarding the object to the second highest bidder. Ask whether raising your report can lose you the object. It can, so stop looking for the payment scheme that would make it truthful.
Know these first
Leads on to
When it stops being true
- single-dimensional-types
Easily confused with
Sources
- Myerson, R. B. (1981). Mathematics of Operations Research 6(1), 58-73.
- Krishna, V. (2002). Academic Press.
- Riley, J. G. and Samuelson, W. F. (1981). American Economic Review 71(3), 381-392.