Some information from Wikipedia about US Electric Lighting Company:
Hiram S. Maxim started a lightbulb company in 1878 to exploit his patents and those of William Sawyer. His United States Electric Lighting Company was the second company, after Edison, to sell practical incandescent electric lamps. They made their first commercial installation of incandescent lamps at the Mercantile Safe Deposit Company in New York City in the fall of 1880, about six months after the Edison incandescent lamps had been installed on the steamer Columbia. In October 1880, Maxim patented a method of coating carbon filaments with hydrocarbons to extend their life. Lewis Latimer, his employee at the time, developed an improved method of heat-treating them which reduced breakage and allowed them to be molded into novel shapes, such as the characteristic "M" shape of Maxim filaments. On January 17, 1882, Latimer received a patent for the "Process of Manufacturing Carbons," an improved method for the production of light bulb filaments which was purchased by the United States Electric Light Company. Latimer patented other improvements such as a better way of attaching filaments to their wire supports.

In Britain, the Edison and Swan companies merged into the Edison and Swan United Electric Company (later known as Ediswan, which was ultimately incorporated into Thorn Lighting Ltd). Edison was initially against this combination, but after Swan sued him and won, Edison was eventually forced to cooperate, and the merger was made. Eventually, Edison acquired all of Swan's interest in the company. Swan sold his United States patent rights to the Brush Electric Company in June 1882. Swan later wrote that Edison had a greater claim to the light than he did, in order to protect Edison's patents from claims against them in the United States. In 1881, the Savoy Theatre became the first public building in the world to be lit entirely by electric lights.

Besides Edison there were other strong competitors like Stanley, Brush, George Westinghouse (Union Switch & Signal Company since 1883, in 1886 becoming Westinghouse Electric Company), Sigmund Bergmann (Bergmann & Co. in 1982), Thomson-Houston Electric Light Company, Perkins, and many others started inventing incandescent lights, sockets, switches and many other electrical parts. But also the side of power had to be developped: In 1876 Charles Brush designed his first Dynamo which would power a single Arc Light which was granted a patent in April 1877. William Stanley invented the self regulating Dynamo. There were also the Gramme and the Wallace generators.