The pipe set was made by the Robert M Prophet Pipe Company (hence"RMP"), which was the "exclusive manufacturer of United States Meerschaum Pipes" per a snippet in the March 27, 1915 issue of Tobacco. The founder, Robert Mathias Prophet, was an active (presumably apprentice) meerschaum carver as early as the 1880 census, when he was 15 years old. Born in NY, Prophet was in the Boston area by 1894 and remained there through 1897 working at Ehrlich's shop on Court Street. In 1898 he moved to NY/NJ, where he worked for one of the many manufacturers located in the area. By 1910 Prophet was listed as a pipe manufacturer, and presumably in business for himself. His son Robert M Prophet junior was intermittently involved in his father's business, but from the twenties on was more active in the emerging opportunities as a dealer in automobiles. Robert senior was still associated with smokers articles as late as 1926. Along the way he found time, in 1920, to apply for and receive a patent which described an improved method of attaching removable bowls using a push instead of the usual screw; the patent was assigned to Reiss-Premier.
Given the above, as well as the materials used, my guess would be the pipes listed on eBay date from the teens.
