Air carrier Captain reported a ground conflict with another air carrier while taxiing at MIA airport.

Narrative

After landing on 26R in MIA; and cleared to cross 26L; Ground instructed us to taxi to the gate via M and W to gate. Turning onto taxiway W Aircraft Y flight that was told to give way to us; did not give way. My FO (First Officer) was clearing the turn when he noticed Aircraft Y and directed me to stop. I immediately and abruptly stopped the aircraft as Aircraft Y taxied by us. Spacing was close and it didn't appear that Aircraft Y slowed down at all. Ground admonished the Aircraft Y pilot and apologized to us. I then called back to the Flight Attendants to make sure nobody was standing and to make sure no one was hurt. I was told no one was up and that no one was hurt. I was taxiing slowly as we were very early arriving in MIA. The FO was looking out the window during the turn and informed me as soon as he was able. It's possible that Ground Control could have noticed this happening and given us a warning. But; the Aircraft Y pilot should have yielded. This was a very close call. Also; with my abrupt stop; people could have been hurt. Maybe Ground Control could have made sure that the both aircraft were aware of each other.