Air Carrier Captain reported a critical ground conflict during arrival taxi with another air carrier approaching the same intersection. The Captain queried ATC and was directed to give way to on coming aircraft.

Narrative

After landing on MCO Runway 36L and exiting the runway at taxiway Y; we were cleared by the MCO Tower Controller to 'Cross Runway 36R on Y then contact Ground Control'. While crossing Runway 36R; which was active and being utilized for departures; I saw an Aircraft Y taxiing South down taxiway B toward the intersection of B and Y. The aircraft did not appear to be slowing down and was about to cross my path on B. I could only assume that the Aircraft Y was communicating with MCO Ground frequency and had been cleared to taxi South on B with no hold short instructions. I made the decision to slow my aircraft considerably while crossing Runway 36R to avoid colliding with the southbound Aircraft Y. This involved slowing to an almost complete stop prior to completely clearing the hold short line clear of Runway 36R while calling Ground Control; as there is not enough room after clearing the hold short line to allow an aircraft to pass on B. Upon calling MCO Ground Control; we were instructed to 'give way' to the Aircraft Y (which we of course had already done to avoid a collision). I can only assume that Aircraft Y; like us; had not received any hold short instruction or been instructed to give way to our aircraft. After receiving the instruction to give way to the Aircraft Y before proceeding to the ramp; I noticed an Aircraft Z departing 36R directly behind our aircraft; which was extremely close to not being completely clear of the hold short line of the active runway. From the sound and attitude of the Ground Controller; I do not think they realized or truly appreciated the near collision that had just been avoided. In this situation; if both aircraft would have followed MCO Tower Control and MCO Ground Control clearances as instructed; we would have collided at the intersection of taxiway Y; B6; and B. The coordination (or lack of it) between the MCO Tower Controller that cleared us across the runway and the MCO Ground Controller that cleared Aircraft Y to taxi South on B was conducted in a way that put us both in danger of an imminent taxiway incursion. This would be the first of two near incursions I would experience on the same day within just a few hours at the same exact intersection due to this poor coordination between the Tower and Ground Controller (once while arriving and one departing).