Individual rationality
The requirement that taking part in the mechanism leaves every participant at least as well off as staying out of it.
Often misread asRunning it together with incentive compatibility, so one check is thought to cover both, when they constrain different decisions: whether to take part at all, and whether to be honest once you are in.
How to see it
Nobody can be made to take part
Participation is voluntary, so the rules must leave each participant at least as well off as they would have been by staying out. What staying out is worth is fixed outside the mechanism, by the person's own outside option.
The checkThey are separate constraints and a mechanism can satisfy either without the other. Most of the impossibility results in this area come from being unable to satisfy both at once alongside a balanced budget.
Try itA seller is asked to hand over goods at a price below their cost under rules that make honesty optimal. Say which constraint that breaks. It is participation, and no amount of truth telling repairs it.
Know these first
Leads on to
Easily confused with
Sources
- Myerson, R. B. (1981). Mathematics of Operations Research 6(1), 58-73.
- Myerson, R. (1991). Harvard University Press.
- Laffont, J-J. & Martimort, D. (2002). Princeton University Press.