Who will win the Battle of the Batty? In Woolly Mammoth Theater’s production of The Gigli Concert, each character is a contender.

In one corner we have the fidgety, self-absorbed and ultimately nutty J.P.W. King (Howard Shalwitz), practitioner of Dynamatology, a pseudoscience never fully explained, which comes off as a nonsensical marriage of philosophy and psychology. There’s Mona (Kimberly Schraf), the sexually aggressive adulteress chatting with a young girl who doesn’t appear to be there. And let’s not forget the volatile Irish stranger (Mitchell Hébert) consumed with the desire to sing as well as Italian tenor Gigli.

The stranger wanders into King’s office skeptically seeking his services after rejecting the treatment of an average shrink; the stranger’s violent temper and inescapable depression is worrying those around him. King, whose roster of patients is essentially nonexistent, is all too eager to take on the challenge, though the effort becomes part vanity project and part couch session for the doctor himself. Their sessions at first, while frustrating in their meandering nature, are interrupted by moments of humor and character insight.