B737-800
Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe; Deviation - Altitude Excursion From Assigned Altitude
Flight Crew Took Evasive Action
Aircraft
Flying at FL360 we received a traffic warning. It appeared at the same altitude and directly in front of us heading towards us on our MFD's. We received the 'climb climb' alert; and immediately began a hand flown climb. We climbed to FL370; and the traffic disappeared off the MFD.  We never received the 'clear of conflict' annunciation. We had advised ATC of our deviation as we were climbing. We returned to our assigned altitude soon after. ATC reported no known traffic in the area. This appeared to be a false warning. The night was clear; and we saw no traffic anywhere near us.
B737-800 First Officer reported receiving a false traffic alert at FL360 with no traffic in the area.