MEM GND CTLR WITNESSED GND CONFLICT THAT REPORTEDLY OCCURRED BECAUSE CTL ISSUED INSTRUCTIONS TO THE WRONG ACFT.

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I WAS WORKING GND CTL #1 DURING THE ARR PUSH AND WITNESSED THE FOLLOWING EVENT TAKE PLACE INVOLVING LCL CTL #2 AND GND CTL #2. MEMPHIS WAS IN A N CONFIGN; LNDG RWY 36L AND RWY 36R; DEPARTING RWY 36C. GND CTL #2 TAXIED A HAWKER JET SBOUND ON TXWY Y WITH THE INTENTION OF XING RWY 36C AT TXWY P AND CONTINUING S ON TXWY S TO THE APCH END OF RWY 36C. THE PURPOSE OF THIS TAXI RTE WAS TO SAVE THE PLT SOME TIME. NEW AMASS WAS OTS AND WE DID NOT HAVE THE STAFFING TO OPEN LCL CTL #3 SO THAT RWY 27 COULD BE USED; WHICH WOULD HAVE ULTIMATELY SAVED THE HAWKER JET EVEN MORE TAXI TIME. GND CTL #2 HAD PREVIOUSLY TAXIED AN LJ35 TO RWY 36C VIA TXWYS Y; A; B; AND S; TO AVOID TFC LNDG RWY 36R THAT WOULD TAXI VIA TXWY Y. LCL CTL #2 COORD WITH GND CTL #2 TO HAVE THE TFC SBOUND ON TXWY S 'GIVE WAY' TO A DC9 THAT HAD JUST LANDED ON RWY 36R AND WOULD EXIT THE RWY AT S4 AND THEN CROSS RWY 36C AT TXWY K. GND CTL #2 PROVIDED 'GIVE WAY' INSTRUCTIONS TO THE WRONG TAXIING ACFT AND THE UNAFFECTED ACFT ACKNOWLEDGED THE 'GIVE WAY' INSTRUCTIONS. THE DC9 EXITING RWY 36R AT S4 AND THE LJ35 AT THE INTXN OF TXWY S AND S4 BOTH CAME TO A SUDDEN HALT; NOSE-TO-NOSE; HAVING PROCEEDED WITH SPECIFIC INSTRUCTIONS FROM THEIR RESPECTIVE CTLRS. AT THIS POINT THE GND CTL #2 CTLR (ALONG WITH EVERYONE ELSE IN THE TWR CAB) REALIZED WHAT HAD HAPPENED. I BELIEVE THAT SEVERAL FACTORS CONTRIBUTED TO HIS NEAR COLLISION: 1) THE GND CTL #2 CTLR WAS WORKING OVERTIME TODAY; AND THIS WAS HIS 6TH CONSECUTIVE DAY OF WORK. 2) THE GND CTL #2 CTLR HAD ADMITTED TO BEING VERY TIRED EARLY IN THE DAY DUE TO LACK OF SLEEP THE NIGHT BEFORE. 4)THE GND CTL #2 CTLR WAS RELUCTANT TO CALL IN 'SICK' DUE TO THE FACT THAT 'LACK OF SLEEP IS NOT AN EXCUSE FOR TAKING SICK LEAVE' (AT LEAST ACCORDING TO MEM MGMNT). 5) AT THE TIME THAT LCL CTL #2 COORD WITH GND CTL #2 FOR THE 'GIVE WAY' INSTRUCTIONS; GND CTL #2 HAD JUST STARTED A POS RELIEF BRIEFING AND BECAME DISTR. 6) THE GND CTL #2 CTLR'S SHIFT WAS DUE TO END WITHIN THE NEXT 30 MINS AND HE WAS READY TO GO HOME. I BELIEVE THAT THE LCL CTL #2 CTLR COULD HAVE HELPED THE SITUATION BY NOT ASKING GND CTL #2 TO 'GIVE WAY' TO HIS ACFT. THE SITUATION WAS SO CLOSE; THAT THE DC9 COULD HAVE EASILY SLOWED HIS TURN SO AS TO PASS BEHIND THE SBOUND TFC ON TXWY S. THE RELIEVING CTLR HAD BEEN WATCHING THE POS FOR JUST A FEW MOMENTS; AND IT'S POSSIBLE THAT A MORE IN DEPTH REVIEW OF THE POS MIGHT HAVE ALLOWED THIS CTLR TO HAVE ASSISTED IN STOPPING THIS ERROR. THE GND CTL #2 CTLR COULD HAVE USED A MORE TRADITIONAL TAXI RTE INSTEAD OF TRYING TO HELP THE PLT TO SUCH A GREAT DEGREE.