David Rabe’s latest play, The Dog Problem, is a dramatic version of the shaggy-canine story as crossed with The Godfather and Waiting for Godot. Moreover, the dog is a member of the cast. Rabe, who made an early reputation in the 1970s with his Vietnam plays — The Basic Training of Pavlo Hummel, Sticks and Bones, and Streamers — and then took on coked-up Hollywood in Hurlyburly, writes about ordinary people who seem to have nothing more on their minds than trolling for their next beer. Yet the characters’ lines are often studded with existential questions about the meaning of life, and these make the dialogue sound like poetry.

More recently, Rabe has focused on the garden-variety hoodlums who populate the fringes of organized crime. He seldom writes about the bosses, just the guys they’re driving in a futile chase after the chimæra of the American dream. Those the River Keeps (which the American Repertory Theatre produced in 1994), about a gangster trying to escape from his past, was not a critical success, but I was moved by Rabe’s sympathy for the plight of the loser at the play’s center.

The New England premiere of The Dog Problem, at Wellfleet Harbor Actors Theater, suggests that the playwright is more interested in exploring retribution for his characters’ decisions than in constructing a sophisticated plot line. The play takes place mostly on the street corners of Lower Manhattan. (An earlier version of the work was performed at the Williamstown Theatre Festival in 1998, under the name Corners.) There a loosely connected group of neighborhood thugs meet in a confrontation that ends in an unusual gangland-style assassination. Ray has taken Teresa to bed for a one-night stand that his dog either watched or participated in — depending on whose version of the event you believe. Teresa incites her brother Joey to avenge her honor; Joey, a dim bulb, brings his Uncle Malvolio, a neighborhood version of a mob boss, into the picture. Other characters include Ronnie, who has psychic powers he can’t explain; Tommy Stones, the refrigerator-sized bodyguard to the ailing Uncle Mal; and the Dog, here played by a winsome English Lab named Blu Bradford. There’s also a Catholic priest who wanders about in the park at 4 a.m. and hears confessions on demand.

The nature of friendship, the importance of loyalty, and the quest for safety in a cosmic sense are issues that hover beneath the surface of the sometimes guttural exchanges and transform into flights of metaphor in monologues by several of these hapless folks. Rabe plays on clichés that have been planted in our minds by countless films and television shows, but he twists them to undercut our suppositions. Ronnie seems like a dweeb, but he also utters Cassandra-like prophecies that are too urgent to be ignored and that stir up subterranean desires in the other characters. Uncle Malvolio aims to rub out men’s souls, not merely their bodies. Although there are many comic lines, director Jeff Zinn captures the frantic roll of the undercurrents Rabe has set boiling in his men. Like most of the women in the plays of David Mamet, the oversexed Teresa is underdeveloped and generally a cipher.

Thomas R. Kee as Ray, the patsy in a situation that spins out of control, is superb in the range of emotions he travels in his attempts to save his life. Marc Weiss as Uncle Malvolio veers from barking orders at his underlings to barking orders at the moon peeking out from under the clouds, then thinking better of his behavior. The scene in which he tries to cut a deal with the priest for absolution is a wonderful mix of faith, impiety, and chutzpah, even though Michael Saari’s priest is the one weak link in the cast. Although there are inconsistencies in the way they decipher the motives of the playwright, the splendid actors at Wellfleet nonetheless present a believable group portrait of men in crisis dogged by their too-human flaws.