Who Pays for the "Nudge"?

The NY Times has a fun piece focused on a Stanford Prof named Balaji Prabhakar.  Dr. Prabhakar seeks to reduce traffic congestion at Stanford University and has figured out a clever nudge for how to achieve a separating equilibrium.  Commuters to Stanford's campus have private information concerning their own desire to arrive on campus at "rush hour" (say 8am to 9am).  Some faculty and staff are in no rush to arrive then while others have a great desire to arrive at that time.

Due to the tragedy of the commons (the roads are common property) traffic congestion ensues as the spike in private vehicles congests the roads.  The typical Econ 101 solution to this problem is to impose a time of use fee such that if you arrive in some "central commuting district" at rush hour that you must pay a congestion fee.  This "solution" nudges drivers who can travel off-peak to reschedule their trip and this in aggregate solves the congestion problem.  But, nobody likes paying this fee.

Enter, Dr. Prabhakar's solution --- the subset of Stanford drivers who choose to drive off-peak are now entered in a lottery and can win a cash prize.  Using Facebook and Social Media, they can show off to Stanford friends that they won the lottery.   At least two questions arise:

1.  Who pays for the lottery prizes? How is this solution "sustainable"?   It appears that grants from the U.S DOT provide the "sugar daddy" cash.  The beauty of a congestion charge is that the "polluter pays" and money is collected. This Professor's scheme exports $ back to lucky lottery winners.

2.  How does Dr. Prabhakar know that he isn't awarding lottery tickets to people who didn't plan to commute at the peak hour?  You only want to give a coupon to those who were just at the margin of buying the product or not.  A firm is wasting $ when it gives a coupon to someone who always buys the product or never plans to buy the product.   He might counter that his information technology allows him to know who is  a peak time commuter but people may drive in a few times at that hour to qualify for the lottery.

3.  As his program succeeds and more people switch over to driving off-peak, each person's probability of winning the lottery declines. If they know this, will they substitute back to peak time driving? Or will the Prof increase the number of winning lottery tickets? If he does this then #1 discussed above becomes more important!  So, for his program to be sustainable --- he either must have a sugar daddy to pay for the prizes or hope that the Stanford faculty can't calculate probabilities!  Funny!