B737-800 Captain reported a ground conflict with two aircraft while taxiing to the gate after landing.

Narrative

Day 0 (approx. XA:40) Aircraft X ZZZ1 to ZZZ. After landing on runway XXR at ZZZ and initial taxi instructions; we were instructed by ground control to taxi to taxiway 1 via taxiway 2. My FO contacted ramp control as we approached taxiway 1. Ramp control cleared us to taxi to our gate XX east line. After our instructions to taxi to gate XX east line via taxiway 1 we heard a radio transmission on ramp frequency for Aircraft Y (an airbus I believe) to taxi on to the east line into the alley and that Aircraft Z was presently on the east line but shortly would be transitioning to the west line to depart the ally. I stopped our aircraft on the throat (taxiway 1) as it wasn't clear if Aircraft Y (airbus) was to yield to us or if we were to yield to the airbus. The airbus kept moving and taxied into the alley on the east line and stopped unable to proceed to their gate because the Aircraft Z was still on the east line ostensibly busy starting engines. Since it was apparent we were not going to be able to enter the ally; I called ground to inform them that the alley was blocked. I knew there was an aircraft ('Aircraft A' as I recall) following us on 2; so I wanted to contact ground in case they needed us out of the way. Ground instructed us to turn left onto taxiway 3 and hold short of taxiway 4.As my FO and I checked clear left/clear right" prior to our left turn onto 3; we observed Aircraft B taxiing on 3 approximately just past the abeam point of taxiway 5. There was no instruction for Aircraft B to 'give way' to us nor was there an instruction for us to follow Aircraft B. Aircraft B was not slowing down. His taxi light was illuminated. Therefore; it was apparent Aircraft B was determined to keep moving down taxiway 3.We remained stationary. The radios were busy and as Aircraft B approached it appeared to me that his wingtip would hit the right side of our cockpit if he didn't stop or maneuver around us. We did not have time to inquire as to whom was to give way. I simply made a radio transmission; 'Aircraft B needs to stop!'. Aircraft B did not stop. Aircraft B maneuvered around our aircraft turning right slightly into the alley as we remained parked on taxiway 1. I estimate Aircraft B's wingtip was 3-5 yards in front of the nose of our aircraft as he passed in front of us. After Aircraft B cleared; I instructed ground control we were proceeding onto 3 behind Aircraft B.No taxiway incursion occurred and we all continued uneventfully. However; had we simply followed instructions there were two times in a short time span that an incursion was immanent; once being cleared into the ramp at the same time another aircraft was cleared into the alley; and another being cleared onto taxiway 3 as Aircraft B was taxiing in our direction on 3. Fortunately; my First Officer (a strong pilot) and I maintained situational awareness and did not proceed without a clear understanding as to who was to follow whom in both cases.Cause: Primarily; ramp control clearing two aircraft into the alley simultaneously created a scenario for a potential ground incursion. From my perspective; ramp could have informed one of us (either our aircraft or the Aircraft Y) of the congested alley and to hold off and contact ground control for 'circle back' instructions. Another option; due to Aircraft Y's gate being deeper in the alley than our gate; have Aircraft Y hold on 3 prior to the alley as we taxied into gate XX as it appeared there was room for us to taxi safely to gate XX with Aircraft Z on the east line. By the time we taxied into the gate Aircraft Z would have been ready to taxi onto the west line and Aircraft Y would have a clear ramp to taxi to their gate. Additionally; the expectation and operational 'push' to 'keep it moving' at ZZZ while taxiing counterclockwise on taxiway 2 and clockwise on taxiway 3 is the current practice. And this practice makes pilots reluctant to stop which led to Aircraft B's wingtip nearly clipping our cockpit. Perhaps training and improved tools would aid in efficient sequencing and communication to provide better coordination amongst aircraft; ramp and ground to mitigate events like the one we experienced on Day 0.Finally; the missive from Company A 'ZZZ Ground Congestion' to pilots stressed 'efficiency' not safety. The section labeled 'Minimize alley time' pushing pilots towards single-engine taxi creates more hazards without solving the root cause(s) of congestion. Jet blast in an already congested alley is dangerous to ground personnel. Putting a first officer 'heads-down' while taxiing is a bad idea when 'heads up' outside scanning mitigates collisions. Adding additional workload during one of the most critical phases of flight at a high operations tempo airport will cause task saturation for the flight deck and lead to errors that sets up crews for failure. The mention of adjustments to scheduling banks and investments in technology should be part of the multifaceted efforts to reduce congestion. Nevertheless; the primary focus needs to be preventing ramp/taxiway incursions. Ultimately; this will result in a safer and more efficient operation."