What is the conflict in Pirandello's play Six Characters in Search of an Author?

There are actually several conficts within Pirandello's
play. The conflict that sets the plot in motion is that between the author and his six
characters. As the play begins, the characters directly address the audience to announce
that they are on stage to look for a new author to complete their story as the one who
created them has left their story incomplete. The characters also create a contrast with
the actors wh will eventually come to embody them. They think they are more "authentic"
than the actors. This initial situation creates a sense of conflict between reality and
illusion, which is the main theme of the play. Like several other Modernist works,
Six Characters in Search of an Author calls attention to its own
fictional devices, dismissing, in spite of its characters' claim on their authenticity,
all realistic pretences.

In addition, there are important
conflicts among the six characters themselves: the Son is resentful against his father
and his adoptive family; the Step-daughter, in turn, dislikes her step-father (whom she
meets in the brothel where she has to work) and the Son because of his
contempt.