Grandma
The sardonic and witty commentator of the play, Grandma is somewhat marginalized from the central action of the household and, from this vantage point, comments upon the spectacle, seemingly aware that she is in a play. Her advanced age allows her to be further isolated from Mommy and Daddy's dialogue due to bouts of (potentially feigned) deafness and senility. It is precisely due to her separation from the others that she is able to recognize the absurdity at the heart of the play.
Mommy
The domineering matriarch of the household. Mommy is a violent and sadistic disciplinarian, serving as an exaggerated stereotype of a bad mother. Through scorn and sarcasm, she dismisses Grandma and emasculates Daddy. Furthermore, she was responsible for the mutilation and death of their child after objecting to its behavior.
Daddy
A pitiful figure emasculated and infantilized by the sadism of Mommy. He relies on her to validate his masculinity and searches for punishment, becoming masochistic and infantile.
Mrs. Barker
A volunteer from the adoption agency that gave Mommy and Daddy their child all those years ago. She appears entirely ignorant to the nature of her visit and the machinations of the household.
The Young Man
Seemingly an archetypal ideal American young man, dubbed "the American Dream" by Grandma. Grandma works out that he is the twin of Mommy and Daddy's adopted child, and was rendered unfeeling and incapable of desire because of his twin's mutilation. As such, he is beautiful on the outside but empty within, serving as a representation of the eponymous 'American Dream'. He serves as a substitute for his twin, taking his place in the dysfunctional household.