Flight crew reported during taxi they observed a service vehicle driving fast and coming towards them. They had to apply brakes to avoid a collision.

Narrative

As we were cleared to taxi and started moving; a service vehicle came from our left. He passed the aircraft at the gate next to us as we were cleared; and kept coming at what seemed a high / unsafe rate of speed. Person A said 'watch this guy' and as we turned away from him; I hoped he would stop prior to entering the safe zone around the aircraft; but he did not. He kept coming; I looked him in the eye and saw that he saw us; but I had to get on the brakes hard to avoid a collision. Just after I hit the brakes; he also hit the brakes; coming to within less than 10-15 ft. of a collision. He then backed up and we continued our turn out. Reported to the Ramp Controller that 'Vehicle X' was the vehicle that did not yield. I cannot say for certain if this driver was looking at his phone or not but it seemed he was not paying attention.Suggestions: Re-educate this driver in reference to driving rules on the ramp and to maintain vigilance. Keep track to insure this driver does not do this sort of thing again. If this driver has been involved in this sort of situation before; perhaps it's time to cancel their ramp driving privileges.