What’s the fair price — carpooling across the Bay Area Bridges?

My colleague, Thomas Tan, has a pricing dilemma that is worthy of Steven Levitt’s (of Freakonomics fame) attention….

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??

Thomas’ math:

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?