The Website Old radio parts dated it to the 1920s.. But there's enough information here to narrow that down I believe. Milton Bradley made a few radio board games including one themes for Fibber Mcgee. There was another game #4674 which may even be a revamped version of the one above. The Elliott Avedon of the Virtual Museum of Games wrote the following about his own copy of this game.
"As has been pointed out by game ethnologists, one of the things people seem to do to become comfortable with new technology is play with it, or play a game based upon the new technology! And so it was with radio in the early years of the 19th century. A number of games in playing card format and boxed board games appeared on the market concerning the subject of radio."Game play is made clear by the directions. The game board is a stylized map of the United States indicating the boundaries of each State, time zones and the rough locations of about 55 radio stations. Some of these locations are a bit off. For example, KPO a San Francisco station is positioned over the Mojave Desert. The distribution was probably somewhat altered to avoid clutter. Red and blue lines connect strings of stations probably as a quiet reference to the Red and Blue NBC Networks, thought the member stations do not match. The time zones on the map are identified by colors matching the pieces: Red is Pacific Time, Green is Mountain Time, Blue is Central Time and Yellow is Eastern Time. The pieces match those colors so that a spinner can determine turns and movements.
The calls on the map are as follows: KTW, KFIF, KFDJ, KFFR, KPO, KFDH, KZN, KFAU, KFBB, KFDO, KFBU, KFEL, KFDH, KLZ, WCAT, KFJM, WLB, WCAL, WOI, KFKX, KFHX, WKY, WRAA, WFAA, WIAO, WOG, KYW, WRAF,WWJ, WTAM, WHAS, WCBQ, WOK, KFNG, WAAC, WBY, WMAZ, WABI, WCAX, WBZ, KDKA, WOO, WNYC, WBBL, WBT, WQAZ, WOAH, WSB, and WDAE
Every source I read dates it to the 1920s, some more specifically to 1925. Using the call letters we can get much more specific. Milton Bradley was incorporated in 1860, much too early to give us a start date. So I'll start with 1060 KYW-AM. The map put KYW in Illinois, which was accurate in the 1920s. KYW went on air in Chicago in 1921. So this can be no older than that. In 1934 clear channel assignments moved it to Philadelphia so the game must have been conceptualized in that 13-year window. KFIF went on air in March of 1923, WABI was a bit later in May of 1923. WFAA on June 26, 1922, KLZ, WHAS, WMAZ and WLB were in 1922 as well. that gives us somewhat of an early number.
My best guess on the late date is based on KFHX and WIAO. They date to 1921, with the latter changing calls to WSOE in August of 1924. Now we're down to a window that clearly predates the 1925 estimate. The list must of call letters used in the design of the game must have been compiled in the 14 months between May of 1923 and August 1924.