The sentence “a quiz show is about contestants competing each other.” is grammatically incorrect. The correct form is:

A quiz show is about contestants competing with each other.

Why “with” is needed

In English, the verb compete usually takes the preposition with (or against) when talking about people in opposition.

  • Correct: Contestants compete with each other.
  • Also correct: Contestants compete against each other.
  • Incorrect: Contestants compete each other.

So, your title should be something like:

  • A quiz show is about contestants competing with each other.

This keeps your original idea but fixes the grammar.