As you might know, the cost of using the Bay Area’s bridges has gone up as of July 1, 2010. As you might also know, cars with 3 or more passengers (“car poolers”) until recently drove across for free. Now, they get to pay between $2.50 and $3.00 to FasTrak.
While it is still clear, from a game theoretic perspective, that carpooling is the way to go, poor Thomas, who regularly picks up a few car poolers while crossing the 4.5 mile long Bay Bridge, was left wondering what is a fair distribution of the $2.50 fee??
Cost if everyone went their merry way: $6 + $2 (toll + cost of ~4 miles) for the driver, $4 (for a BART ticket) for each of the carpoolers = total cost of $16.
An equitable distribution suggests that the $4.5 ($2 for using the car and $2.5 for tolls) be split as $2.25 (driver) and $1.125 for each of the 2 carpoolers.
My take, close but more simple minded:
Keep the math simple, use whole amounts to simplify the transaction, and let the driver use his FastTrac device to pay $0.50 and let each of the carpoolers pay $1 each. I assume that the cost of driving across the bridge is a sunk cost, as it will not go away in either case.
(Better) Ideas for Thomas, anyone?