Backgammon was one of the very first Coco 1 cartridge games released by Radio Shack. Unfortunately, there is no title screen per se, so I have no idea who wrote it, although the manual states that is was actually made by Tandy.
Title: Backgammon
Author: ??? (Tandy Corporation)
Publisher: ??? (distributed by Radio Shack)
Released: March 1981
Requires: Color Computer 1,2,3, 4K RAM, cartridge, joystick optional.