# Touch the Truck

There was a British game show in the early 2000s called “Touch the Truck,” where, according to the rules, the truck would go to whomever could keep his hands on it the longest. Similar games have been featured in a number of other shows, including Survivor, where the last person to keep his hand on the totem would win immunity and That 70’s Show, in the following episode (start at 3:37 — you don’t need to watch the whole episode, unless you want to):

The three games that I’ve just mentioned differ in a couple of ways. In the British show, the contestants are able to take breaks, and are disqualified if they fall asleep, so it is primarily a contest of sleep-deprivation. In Survivor and That 70’s Show, bathroom breaks are not allowed, so the contest is much shorter and contestants might gain an advantage by wearing (ew) diapers or catheters. Obviously, pulling a stunt like that incurs costs — does the contestant really want to wear a diaper?

We can also think of Touch the Truck as a war of attrition or all-pay auction — any amount of time that the contestants spend holding their hands to the truck is a sunk cost. They’re not getting that time back. In most all-pay auctions or wars of attrition, the outcome can someone be that the players bid more than the object is worth — suppose you auction off a $20 bill, and everyone pays their bid regardless of whether they win. Then, you can imagine a scenario in which someone has bid up to$20, and another player who already has $18 in the game might bid$21 so as to only lose $1 rather than$18. If he wins by bidding more than the value of the object, we call it a Pyrrhic victory.

However, there is a slight (and largely inconsequential) difference between Touch the Truck and most wars of attrition or all-pay auctions. In all-pay auctions, players can bid as high as they like, whereas in Touch the Truck, the human body can endure only so much. The world record for staying awake is something like 11 days, and in most of the latter 8 days or so the person is basically not really functioning. (The longest I’ve ever continuously stayed up is probably around 50 hours, and by then I pretty much can’t do anything.) The truck, however, we can say is worth at least $15,000 — a conservative estimate. So, even if someone were able to stay up for 11 days, and took another 4 days off to recuperate, he has still earned$15K in 15 days [1]. Not too shabby. And, since none of the contestants can actually stay up long enough for the time lost to be equal to \$15K, there will always be additional rent that each contestant can earn (the winner will never have a Pyrrhic victory).

So what’s the equilibrium outcome? Well, the winner’s outcome is similar to the winner’s outcome in second-price auctions or English auctions. Since the contestants have differentiated levels of ability to stay awake, if you’re not the person who can stay awake the longest, then you might as well lose immediately. If you are the contestant who can endure sleep-deprivation the longest, then you should stay up as long (or $\epsilon$ longer) than the second most fortitudinous contestant. You should choose to do it even if no one else is choosing to enter the contest, because if there’s a chance you’ll quit sooner than that, then someone else might be able to win and might want to enter the contest.

Of course, in this example, there is perfect information — everyone knows everyone else’s level of fortitude, etc. The entertainment value comes from everyone’s thinking that they might actually be able to endure longer than anyone else, and of course, this comes at the expense of the contestants. Everyone would be better off if he could reliably and accurately communicate how long he could stay touching the truck, but most efforts at communicating this information are cheap talk (like Daniel does in the show.)

[1] Generally we would have to account for different people’s different valuations of the truck, but, since this is a game show and the organization running the game wants to pick the most enthusiastic bunch of people it can find, we will safely assume that every contestant values the truck at market price.