MDT CREW DID NOT HEAR INSTRUCTIONS TO GIVE WAY TO ANOTHER TAXIING ACFT.

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WE LANDED; TURNED OFF THE ACTIVE RWY; TWR TURNED US OVER TO GND CTL. I WAS TAXIING; THE COPLT WAS HANDLING COM. WE WERE BOTH LISTENING. HE CONTACTED GND AND GAVE OUR GATE ASSIGNMENT. CTLR CLRED US TO TAXI TO THE GATE; A DISTANCE OF ABOUT 1400 FT ALONG THE RAMP TXWY. INBOUND; WE COMPLETED THE AFTER LNDG CHKLIST VIA THE INTERPHONE (WE WERE WEARING HEADSETS). IN ADDITION; I ASKED THE COPLT TO CHK 1 ADDITIONAL ITEM (A YAW DAMPER INDICATION). AS I WAS SPEAKING I HEARD THE SOFT-SPOKEN; FEMALE CTLR SAY THAT THIS WAS THE THIRD TIME SHE HAD TRIED TO CALL US TO GIVE WAY TO AN ACR JET THAT WAS STOPPED ON THE RAMP TO OUR L. BY THIS TIME WE WERE ABEAM THE JET; WHO WAS SOME 500 FT OFF OUR L; HAVING JUST TURNED OUT OF PARKING. NEITHER THE COPLT NOR I HEARD THE INITIAL CALLS. I DO RECALL HEARING AN EXCHANGE ON THE FREQ WHILE WE WERE COMPLETING OUR CHKLIST; BUT I DID NOT HEAR OUR CALL SIGN; NOR DID THE INSTRUCTIONS REGISTER AS APPLYING TO US. I DO SUPPOSE THAT I WAS PRE-CONDITIONED TO NOT EXPECT ANY FURTHER INSTRUCTIONS; BECAUSE OF THE SHORT DISTANCE TO THE GATE; THE ORIGINAL 'CLRED TO THE GATE' INSTRUCTION; AND THE LACK OF ANY OBVIOUS CONFLICT BTWN US AND THE PARKING ARE. WE CONTINUED TO THE GATE. THE JET TAXIED BEHIND US. WE RPTED THAT WE HAD NOT HEARD THE 'GIVE WAY' INSTRUCTION. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: CALLED RPTR TO ASK HIM IF CONVERSATIONS ON THE INTERPHONE BLANKED OUT ANY INCOMING RADIO SIGNALS. HE SAID THAT NO; IT WAS SIMILAR TO TALKING ON A PHONE; YOU COULD HEAR YOUR OWN SIDETONE AND ALSO THE PERSON TALKING TO YOU.