The Mighty Hogan Art Players is the nickname given by Colonel Hogan to the prisoners of Barracks 2 when they want to make the Germans believe that they are passing along something that is false as fact so that they can either retrieve vital information from their intended victim(s) or to pass along to them some disinformation, which would end up helping the prisoners to complete a mission.
The prisoners, mainly Newkirk, LeBeau, Carter and Kinchloe, when they are involved, act as though they are performers in a play who have been given assigned parts. The term is first used in the episode, The Prisoner's Prisoner, when Hogan and his men are trying to get from General Schmidt the location of a German division so that they can past the information on to London, so that they can, in turn, use that information to destroy it. The Players would perform in several more episodes during the series' six years run.
The term is possibly a tribute to "The Mighty Allen Art Players" of the 1930s and 1940s. The group, which was created by comedian Fred Allen as a comedy sketch act on his comedic radio programs of the period. Allen's players would perform comedy skits as well as satires of popular films and musical comedies of the day, such as Oklahoma!. It might have also been a tribute or spoof of the The Tonight Show Staring Johnny Carson troup, "The Mighty Carson Art Players", which spoofed the news, movies, television shows and commercials during the years that the show was led by Johnny Carson.