Most, if not all, cab drivers cannot take possession of items left in the cab. New York, for example, says:
§54-18(a) Inspection Following Trips from Airports. Immediately after completing a trip to Kennedy, La Guardia or Newark Airports, the Driver must inspect the interior of the Taxicab and the trunk compartment, if used, to ensure that Passengers have collected their property.
§54-18(b) Handling of Lost Property. Property found by a Driver in a Taxicab must be returned to the Passenger if possible; otherwise, it must be taken without delay to the police precinct closest to where the Passenger was discharged.
§54-18(c) Notifying Commission Regarding Lost Property. If the property is not returned to the Passenger, the Driver must promptly inform the Commission of the details regarding the found property and the police precinct where it is held.
Note that 54-18(b) is not inclusive of (a), but only when transporting passengers to the listed airports is an inspection of the passenger area for lost or misplaced items required. If any items are found outside of those conditions, they still must be taken to the closest precinct, and the Taxi commission must be notified of the property and to which precinct it is located.
It is not the responsibility of the cab driver to track you down, outside of yelling at you while you are walking away from the cab. After that, it is your responsibility as a passenger with a lost item to track it down.
Fun factoid... NYC has $89,000 in lost cash that was turned in and not yet claimed:
"The most "profitable" month last year was June, when New Yorkers turned in more than $15,000 in lost cash to the LPU (only $1,807 was claimed that month).
For all of 2010, the MTA raked in a total of $106,974. But only 16 percent of that ($17,509) was ever claimed, which means the rest of it (a cool $89,465) is still just sitting in an MTA bank account."
Umm... this whole conversation is about GPS tracked devices, almost all of which have strongly linked identifiers. If it's money, then it is a lot harder... not that we were even talking about that, but true statement.
A harder question becomes: I just bought the phone, and I left it in the cab. I can't track it's location, but I kept the cabbie ID number. How can I prove the boxed phone is mine? It's not activated, and the store didn't write down the serial number. At that point, like the previous poster said, it's probably "posession rules, losers drool" and I would lose my phone. Also not entirely germane to the conversation, but interesting thought.
If you left a $100 bill, it's his. No matter how saintly his desire to give it back, there is no way for him to do so, so he may as well spend it.
[Edit: My point is that while I can track the device, the cabbie has no way of tracking me. How could he return the phone to me in this situation?]