Nathaniel Branden was utterly smitten. The year was 1950 and, after reading Ayn Rand's The Fountainhead, the young Canadian from Brampton, Ont., began exchanging letters with the renowned author. With his then-girlfriend, Barbara Weidman, whom he would marry in 1953, he set off to meet Rand and her husband at their home in Los Angeles. By 1954, the famous thinker and her devoted acolyte, who was 25 years her junior, began (with the reluctant permission of their respective spouses) an affair. At first, it was exciting and seemingly consistent with their shared belief that morality is an outcome of rational self-interest. But soon it became a toxic competition about whose ideas were better and who was dominant in the swirling mix of infidelity, betrayal, control and obsession. Three years later, around the time of the publication of Atlas Shrugged, which Rand dedicated to Branden, the affair ended and soon devolved into acrimony.

"Competition corrupts the natural pleasure and the joy of what we are doing," says Branden, now in his 80s and living in L.A. "It takes the joy out of work, out of life, if you succumb to it. It is anti-life." The psychotherapist and author explains: "I competed with Ayn and her understanding of human psychology and that was a mistake. Love isn't winning an argument."

This anecdote is one of several in a fascinating new book, A Bigger Prize: How We Can Do Better than the Competition, by Margaret Heffernan. The idea that competitive self-interest ultimately benefits everyone is sacrosanct. It is part of the collective psyche and manifests itself in everything – the raising of children, the education system, entry into prestigious universities, the operation of businesses, the conduct of sports and the pursuit of love and sex with the "prize" being a wedding.

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Heffernan, an American entrepreneur, chief executive and author, dares to question the competitive imperative in what one reviewer called a "brave exercise." She acknowledges Western cultural background, citing social Darwinists, who believe that if we are the product of an evolutionary contest, the sharpening of elbows is integral to how we function as healthy, progressive society. In the introduction, she slyly points out that the former Soviet Union "incited competition regularly and viciously in all walks of life," lest she be seen as a communist for questioning a central edict of capitalism. Her point: "We are all competitive, but we are not only competitive."

This book comes at a crucial moment. The competitive instinct – to the exclusion of other ways we can behave as a group – has been ramped up in the last 50 years, she argues. We are encouraged to "dress for success" as if nothing less than the desire to win the top prize, that corner office, that title and the most money at whatever cost suggests mediocrity and underachievement. Among other things, this book can be seen as a comment on Wall Street practices that led to the 2008 financial meltdown. Moreover, we bring up our children to compete for the best marks. Such is the culture's embrace of the idea that romantic love is a competition that episodes of The Bachelor fill television screens with a sense of giddy drama and nary a hint of irony. And many want to want to win the war against aging, as if time, too, is something you can triumph over, Botox being the weapon in a fight that humans are not designed to win.

In short, modern life moves to the beat of obsessive competition, but to what end? "We have shied away from the uncomfortable truth that our outsize veneration of competition has left us ill equipped to solve the problems it has created," Heffernan writes. "If we are to invent new ways to live and work together, we need high levels of trust and give-and-take: attributes that competition specifically and subtly corrodes."

Many will see themselves in this book and maybe even cringe. Heffernan starts with the family, showing how sibling rivalry undermines the potential for all involved, encouraging some to be hypercompetitive and others, who are more submissive, to back away from any perceived fight.

She writes about her own father, who was hypercompetitive, the youngest and smallest of three boys. He grew up hating his brothers and left home as early as he could. As a grown man, he was the kind of person others found attractive: charismatic, dynamic, alluring. Think of the high achievers you may know who fit this profile and whom the culture celebrates. We believe that their competitive drive will ensure their success – always. We imagine them in their button-down shirts and shiny ties or their red power suits and heels forever in command, driving the best cars, living in the best homes.

But Heffernan warns us not to make this assumption. There are vast numbers of hypercompetitive people "whose drive subverts them," she suggests. And one, indeed, was her father, who was like many she has encountered in business: "gifted, intelligent thugs." He negotiated agreements with oil companies and governments not to make a workable deal, but to break his opponent's spine, he once told her. And the end result, she writes, was a waste of talent, as the need to triumph excluded the desire for human connection. His employer retired him at the earliest opportunity. And, often, personal relationships suffered.

To be sure, trust and creativity die in a super-competitive culture. No one shares ideas. There's lots of sabotaging in the workplace. And the outcome of that competitive drive doesn't always yield the best result. One example Heffernan gives is that of AutoTune, the world's best-selling audio plugin, which allows music producers to eliminate bad or off-pitch sung notes without changing the timing of the performance. Costly retakes are consequently unnecessary. A wide variety of artists in the the music business have used it. But the technology hasn't made music better. Arguably, it has made it indistinguishable. It's like Photoshop for those wrinkles. Gone are the flaws and idiosyncrasies of the human voice.

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Heffernan is not advocating that we throw out all forms of competition. It is effective in some cases. But because it is, we are tempted to believe that it works in all situations. Gee, wouldn't that be nice? That's partly what I think lies at the root of the competitive urge. We want the chaotic possibilities of life to be simplified. We want some clean answer: Just work hard and fight to win and you will win. If only.

Citing examples of productive, creative companies that are structured as co-operatives and educational systems that are not as competitive – in exams-averse Finland, there is greater academic proficiency, one important study revealed – Heffernan doesn't pretend to be holding out a whole new world order.

All she is really asking is one simple thing: Dare not to think competition is everything in life.