Air carrier Captain reported while turning into their gate they had to stop suddenly to avoid a baggage cart crossing their path.

Narrative

We had entered ZZZ Term X from Spot XXX bound for Gate XX. As we turned off of the northbound yellow ramp line into the gate; one baggage tractor approaching from our right saw us turn right and veered out of the service road. A second tractor; with a baggage cart in tow; came from behind him and failed to yield to us even though we were lined up for the gate and moving forward. The driver never looked left toward the aircraft; but he did look right at the open gate which had a marshaller clearly signaling to the approaching aircraft. I had to briskly stop the aircraft to avoid a collision. The tractor would have hit me since I had nose position on the vehicle.Not only was there a risk of collision; the tractor's failure to yield caused a secondary problem: My First Officer told me after we parked that he heard the flight attendant admonishing people to sit down. The sudden stop followed by the wait for the tractor to pass led people to unfasten their seatbelts; stand up; and begin removing carryons from overheads before we reached the gate. Cause: Tractor driver's failure to maintain a lookout for surrounding traffic and yield to aircraft.Recommendations:1. Recovering ramp crew get out of their shack and be on station BEFORE aircraft enters the ramp so that wing walkers can stop access road traffic when the aircraft arrives.2. Revoke the flight line driving privileges of the driver in question.3. Dock pay of Customer Operations management for each violation perpetrated by the subordinates that they are not adequately training and supervising.