Sleeping games in the car

Jeff Ely gives us the game theory of car sleeping:

Whether it is desirable to have your kid fall asleep in the car goes through cycles as they age.  It’s lovely to have your infant fall asleep in the snap-out car carriers.  Just move inside and the nap continues undisturbed. By the time they are toddlers and you are trying to keep a schedule, the car nap only messes things up.  Eventually though, getting them to fall asleep in the car is a free lunch:  sleep they wouldn’t otherwise get, a moment of peace you wouldn’t otherwise get.  Best of all at the end of a long day if you can carry them into bed you skip out on the usual nighttime madness.

Our kids are all at that age and so its 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.