The thinness of the line between tragedy and comedy can be seen in relation to "The Playboy of the Western World" in several ways. First, if you had to reduce the definitions to the most basic level, a tragedy ends badly and a comedy well. Well, the play does not end badly for everyone. Christy Mahon exits smiling, even if he says, " I am crazy again!" What's more, his position in his community fundamentally changes through the course of the play. He started low and rises, which mostly happens in a comedy.
At the same time, though, Pegeen loses her ideal, her "playboy of the western world." Her world had come together in love (a comic resolution), but seems to have been broken back apart again.
Taking things together, what sort of comic/tragic world is it that a man can brag about killing his own father? Can lie about it? Where a father has to beat his son to be acknowledged?