MD80 FLT CREW EXPERIENCED NEAR MISS WITH ZNY DURING DSCNT.

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AT 13000 FT; RECEIVED CLRNC TO CROSS BEUTY AT 10000 FT AS FOLLOWS: 'CROSS BEUTY AT 10000 FT; TFC DSNDING THROUGH YOUR ALT AT 5 MI. I NEED FOR YOU TO BEAT HIM DOWN.' I SET 1500 FPM AND STARTED LOOKING FOR THE TFC. A TARGET APPEARED AT 11 O'CLOCK POS; CO-ALT; 2 MI. NOTICING THE TCASII TARGET HAD LEVELED; I STARTED A CLB; IMMEDIATELY FOLLOWED BY AN RA DIRECTING A CLB. THE FO XMITTED WE WERE COMPLYING WITH AN RA. THE TARGET PASSED APPROX 500 FT; LESS THAN 1 MI AT 1 O'CLOCK POS. WHEN I MENTIONED THE NEAR MISS TO THE CTLR; HE SAID THAT HE HAD BEEN TRYING TO CALL THE OTHER PLANE AND HAD GOTTEN NO ANSWER AND THAT FOR SOME REASON; THE OTHER PLANE HAD LEVELED OFF. I RESPONDED THAT WE HAD JUST HAD A NEAR MISS AND THAT WAS UNACCEPTABLE AND A SIMPLE VECTOR OFF COURSE WOULD HAVE SOLVED THE PROB. THIS HAPPENED ON A SUNDAY AFTERNOON; VERY LITTLE TFC AND CLR SKY. PHRASEOLOGY; 'I NEED FOR YOU TO BEAT HIM DOWN' AND THE FACT THAT THE PLANE CAN ONLY DSND SO FAST FROM 13000 FT TO 10000 FT AND EFFECT A LEVELOFF AT 10000 FT. IT APPEARED THE CTLR WAS BETTING ON WHAT THE OTHER PLANE WAS GOING TO DO; YET HAD NOT ESTABLISHED COM WITH HIM.