How to allocate an indivisible object to one of three children, it’s a parent’s daily mechanism design problem. Today I used the first-response mechanism. ”Who wants X?” And whoever says “me!” first gets it.
This dimension of screening, response time, is absent from most theoretical treatments. While in principle it can be modeled, it won’t arise in conventional models because “rational” agents take no time to decide what they want.
But the idea behind using it in practice is that the quicker you can commit yourself the more likely it is you value it a lot. Of course it doesn’t work with “who wants ice cream?” But it does make sense when its “We’ve got 3 popsicles, who wants the blue one?” We are aiming at efficiency here since fairness is either moot (because any allocation is going to leave two out in the cold) or a part of a long-run scheme whereby each child wins with equal frequency asymptotically.
It’s not without its problems.
- Free disposal is hard to prevent. Eventually the precocious child figures out to shout first and think later, reneging if she realizes she doesn’t want it.
- There’s also ex-post negotiation. You might think that this can only lead to Pareto improvements but not so fast. Child #1 can “strongly encourage” child #2 to hand over the goodies. A trade of goods for “security” is not necessarily Pareto improving when the incentives are fully accounted for.
- It prevents efficient combinatorial allocation when there are externalities and/or complementarities. Such as, “who’s going in Mommy’s car?” A too-quick “me!” invites a version of the exposure problem if child #3 follows suit.
Still, it has its place in a parent’s repertoire of mechanisms.