Air carrier Captain reported they stopped taxiing to avoid a collision with two shuttle busses.

Narrative

Night operation. Pushed back from Gate XX in ZZZ to spot XX. After engine start; ramp cleared to taxi to hold short of taxiway 1 and contact ground. Taxi light on. Aircraft began to taxi forward on 2 towards taxiway 1. Two shuttle buses (the shuttles that are going between terminal XX and terminal XY) came towards the aircraft (north bound on 2) and drove inside the white line. I stopped the aircraft as it was apparent they were not giving way to us. We watched them both drive under the wing of our aircraft as they proceeded towards their destination. We contacted ramp control and advised them that the shuttles both did not give way and both drove inside the ramp taxiway while we were moving. Once both shuttle buses were clear and we had spoken to ramp control; we continued our taxi.