What does mean exactly "playing the fool" .
Is it as I suppose that someone wants to make beleive to one another that he doesn't understand, or whatever else he is asked ?
I want to be sure, before writing it in a letter.
Thanks for your help.
Your definition is fine.
play/act the fool
1. To act in an irresponsible or foolish manner.
2. To behave in a playful or comical manner.
It also refers to e.g., a business tactic/strategy, to pretend to be stupid in order to make your opponent think you are less of a threat.
In Shakespeare's Twelfth Night, Feste the jester is described as "wise enough to play the fool." Indeed, to be successful in the job of King's Fool the holder had to be anything but a fool in the modern meaning of the word.