When were the college football bowl games started?

Below are some of the bowl games played and the year they started: Rose Bowl: 1902, but then there was a 13 year break. The game started being played every year in 1916.
Orange Bowl: 1935
Sugar Bowl: 1935
Cotton Bowl: 1937
Fiesta Bowl: 1971
Sun Bowl: 1935
Gator Bowl: 1946
Liberty Bowl: 1959
Independence Bowl: 1976
Outback Bowl: 1986
Holiday Bowl: 1978