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A gag character is usually a character that is rarely used, and shows no personality except for the joke in comic strips and TV shows. Often, a gag character's usage is for only one joke.
How a gag character works
Gag characters usually appear in single panel cartoons that do not follow any main character (although they might follow similar types of jokes). Some examples include The Far Side, Bizarro, and Speed Bump. Because of this, gag characters have little to no personality, considering their short lives.
Gag characters also appear on television. However, a gag character on a show usually appears for only one episode. Any subsequent appearances make the character into a secondary character. Occasionally, gags on television are not dubbed "gags". They are more likely to be called stock characters.
A "gag" character in a movie is often referred to as an extra.
However, there are special cases where a gag character can also be the main character of a particular show or a series, in such cases the show follows a single recurring joke throughout the show, unique to that main character, examples of such cases are Arale Norimaki from the Dr. Slump manga and Marvel's Squirrel Girl. Due to being the protagonists of their respective shows, such characters tend to show personality, unlike their standard counterpart. Such characters are also known as Modern Day Gag Characters.