Our kids are all at that age and so it's a regular family joke in the car ride home that the first to fall asleep gets a prize. It sometimes even works. But I learned something on our vacation last month we went on a couple of longer then usual car trips. Someone will fall asleep first, and once that happens the contest is over. The other two have no incentives. Also, in the first-to-fall game, each child has an incentive to keep the others awake. Not good for the parents. (And this second problem persists even if you try to remedy the first by adding runner-up prizes.)
So the new game in town is last-to-sleep gets a prize. You would think that this keeps them up too long but it actually has some nice properties. Optimal play in this game has each child pretending to sleep, thereby tricking the others into thinking they can fall asleep and be the last. So there’s lots of quiet even before they fall asleep. And there’s no better way to get a tired kid to fall asleep than to have him sit still, as if sleeping, in a quiet car.
--Jeff Ely, Cheap Talk, on inverting incentives to achieve optimal sleep outcomes. HT: Marginal Revolution