This is such a clever idea for a novel that it's a wonder no one has thought of it before. Or if they had, perhaps they would have decided against it, because it's so hard to pull off. David Guterson, author of the best-selling and much-loved Snow Falling on Cedars, has written the 21st-century novel of Oedipus Rex, a "myth for our times". Ed King: get what he did with the title? It's the story of a baby boy given up for adoption, who goes on to become one of the world's richest and most powerful men. While, of course, killing his father and sleeping with his mother along the way.

Most of all, though, it's a tale of human error and hilarious idiocy. Ed King's father, Walter Cousins, illustrates this beautifully: he's a self-deluding, well-meaning actuary who ends up sleeping with the au pair when his wife is hospitalised with a nervous breakdown. Oedipus, sorry, Ed, is conceived. The au pair, Diane, is no schmuck, however. She dumps the baby on a doorstep but manages to convince Walter that she is raising the child as a single mother. He coughs up. Walter's hush money allows her to maintain herself in the manner to which she would like to become accustomed. (Quite literally  she ends up having a lot of plastic surgery, allowing her to become young enough to seduce a man her son's age. Clever, eh?)

The baby is adopted by a lovely Jewish couple, Alice and Dan, who name him Edward Aaron King: "Dan, especially, was an Elvis fan." Ed has a relatively normal, if slightly smothering, all-American childhood (his adoptive mother dotes on him). He annoys and is annoyed by his brother Simon and spends his barmitzvah money on a 1966 Pontiac GTO, complete with racing stripes, which he paints on himself. It is while in this car that he has an altercation with another driver, an irritating middle-aged man, whom he runs off the road. (The man is, of course, Walter, who breaks his neck in the ensuing crash.)

By this point in the story we are starting to get the whiff of inevitability, especially as Diane has been quietly remodelling herself for several years now and can easily pass as the sort of woman Ed might go for. Ed himself is destined to become  what else?  king of internet domain Pythia, a search engine. He takes in Stanford on the way and a succession of therapists, who attempt to diagnose his malaise: "And who are you?" "I'm me." "And who is me?"

There are obvious problems with transplanting Greek myth to the digital age, not least sincerity. At times, despite myself, I became invested in Ed King's character, only to find myself feeling annoyed that the author seemed to be mocking him. We laugh at Ed visiting the shrink to get "mental health medication" because we know that his life's trajectory is going to throw him some "lifestyle issues" that are not really possible to medicate away. It's hard to be moved by a story and laugh at its cleverness at the same time.

Guterson certainly had a lot of fun writing this, occasionally, perhaps, too much fun. I bristled slightly during the opening chapters when Diane, then a young, very English au pair, seems to talk with some sort of Dick Van Dyke disorder: "A lass with a lasso, then, for when they're mucking about starkers," she says, describing her role as a nanny. (Who talks like this?) When she asks Walter for a can of beer in the kitchen, she says: "I'll have what you're having. A pint." (Who drinks pints at home?) But it's all to point out that Walter is attracted to her exoticism (and possibly she's putting on these ludicrous anglicisms to seduce him anyway).

Overall, Guterson's way with words and characters is both persuasive and a bit too-cool-for-school. Walter's life was ruined when his wife's "cheesecake magnetism evaporated, never to return". A fortune teller reveals to Ed: "In your present condition you suffer from a terrible inflation, a terrible narcissism, and an overwhelming and dangerous hubris." This really does feel like sniggering at the back of the class.

There is so much going on in this novel, packed as it is with cultural references and knowing winks to the zeitgeist, that it's worthy of several spin-off mini-series. I lost my way a few times but was  mostly  pulled back on course by Guterson's seductive, if occasionally smug, storytelling. And if you're thinking of flipping forward to the chapter "where a mother has sex with her son", Guterson has already got your number. (But it's on page 240.)

Ed King, the self-loving hero of David Guterson's latest novel, is a very rich and lucky man, an entrepreneur who reigns over an internet kingdom called Pythia. This is a search engine that scours the universe to find bits and pieces of information that can, sometimes, transform lives, even the life of the "king" at the centre of this sharply written but flawed novel that has been loosely based (though not loosely enough) on Oedipus Rex.

In most instances, novels based on ancient myths are either magnificent (Joyce's Ulysses) or tedious (Updike's The Centaur), depending on the deftness of the author, who can either refresh the myth at hand by truly reinventing it or simply chug along in its tracks in dutiful fashion, taking all the expected turns. In this case, Guterson allows Sophocles to control his narrative.

This is too bad, as Guterson is a gifted writer. He grabbed the literary world by its collar with 1994's Snow Falling on Cedars, an absorbing novel that became an international bestseller. His subsequent books revealed a risk-taking talent. Certainly The Other, a vivid story about a would-be writer who is left millions by a close friend, appealed to readers on many levels.

The good writing and the bravado are also apparent here. But it's hard to imagine Oedipus Rex as a likely framework for a satire on American values in the 21st century. Guterson himself seems wary of his project. "Okay. Now we approach the part of the story a reader couldn't be blamed for having skipped forward to  the part where a mother has sex with her son." Yet by the time I got to what the author calls "this potential hot part" of his story, I found it difficult to arouse much interest in the sex life of Ed King  or anything else about him.

The book begins in 1962, with a mild-mannered actuary called Walter Cousins, who creepily seduces Diane Burroughs, an English au pair half his age (while his wife lies in a nearby hospital). Diane is "quick-witted and cheerfully combative", though the same cannot be said for Walter. He soon gets the girl pregnant, and she gives birth to a son.

In mythic fashion, she abandons her baby on a doorstep, and much as young Oedipus found himself passed from shepherd to shepherd in Corinth, only to land in the lap of luxury with the king and queen, so baby Ed winds up in good hands, with the well-off King family, Dan and Alice. He becomes the joy of their lives. Alice, in particular, discovers she really loves "the faux suckling, the wiping, the rocking, the holding, the scent of him, the miracle of Eddie".

Guterson can't keep a straight face with this material, and how could he? Everything and everyone is drawn so broadly, with such bold strokes, that subtlety falters.

Ed King in due course goes through various self-inflicted crises, at one point running a gauntlet of quacks and shrinks, such as Dr Paul Stern, who wonders if his patient is perhaps depressed and needs a little help with psychiatric drugs. "Oy," says Stern, when his patient doesn't respond to a pointed question about his circumstances. "I feel terrible for you, Ed. I feel absolutely, one-hundred-percent terrible." Oy, indeed!

Stern prescribes diazepam. This fails, so Ed sees Dr Roger Fine, a proper "head doctor", who delivers this canned speech: "No one likes to be medicated. But when you need medication, it's good it's there." And then comes Theresa Pierce, a stereotypical therapist who "met with clients in a low-ceilinged garret that smelled, to Ed, like old milk in a pile carpet". On and on, the satire rolls, and Guterson hits any number of obvious targets with his poisoned arrows. Some of this is quite funny.

Ed himself is skewered, as when he goes to Stanford and has an 18-year-old's epiphany: "that he wanted to be not only rich and famous, but a historical figure with a huge role on the world stage  like Gutenberg, say, or Galileo." He must, in the end, settle for something like Steve Jobs or Bill Gates.

But the twist here is that he's also Oedipus, belonging as much to Dr Freud as to Sophocles. The mother who adopted him, Alice, won't let him go, telling him flatly at one point: "I don't care how old you get, Ed, you'll always be my baby." Alice has to compete with older women, too: Ed/Oedipus has a thing about them, as he would, given his history. Needless to say, the book takes Ed back to where he started, with Diane.

I hate to spoil the plot, but that's hardly the point. (Brush up your Sophocles if you don't know the story.) It's not difficult to guess in the final pages exactly where the flight of Ed King, in his self-piloted chopper or his magnificent Gulfstream, will take him. Things aren't going to end prettily for the hero; but they will surely end, and that's a relief.